Suppose we want to choose 6 objects, without replacement, from 12 distinct objects. (a) If the order of the choices matters, how many ways can this be done? (b) If the order of the choices does not matter, how many ways can this be done?

Answers

Answer 1

(a) There are 665280 ways of selection if the order of the choices matters.

(b) There are 924 ways of selection if the order of the choices does not matters.

(a)  If the order of the choices matters, then we must use the permutation formula that is

[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]

Here n is the total no. of objects and r is chosen objects

We have n = 12

               r = 6

After we substitute the value we get

[tex]^{12}P_6 = \frac{12!}{(12 - 6)!}[/tex]

[tex]^{12}P_6 = \frac{12!}{6!}[/tex]

[tex]^{12}P_6[/tex] = 665280

Thus, there are 665280 ways of selection if the order of the choices matters

(b)  If the order of the choices does not matter, then we must use the combination formula that is

[tex]^nC_r = \frac{n!}{r!(n - r)!}[/tex]

After we substitute the value we get

[tex]^{12}C_6 = \frac{12!}{6!(12 - 6)!}[/tex]

[tex]^{12}C_6 = \frac{12!}{6! 6!}[/tex]

[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7×6! / 6!×6!

[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7/ 6!

​[tex]^{12}C_6 =[/tex] 665280/ 720

​[tex]^{12}C_6 =[/tex] 924

Thus, there are 924 ways of selection if the order of the choices does not matters.

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Related Questions

Masha bought red, green, and yellow balloons for a party. She bought 40 red balloons. The number of green balloons Masha 3 bought is of the number of red balloons. The number of green 5
balloons is also 2 3 of the number of yellow balloons.
How many balloons did Masha buy for the party?

Answers

Answer:

its 100 ez bro

Step-by-step explanation:

Answer: 100 balloons

Step-by-step explanation:

because it is 100 balloons

Check all relationships

Complementary
Linear pair
Adjacent
Vertical
Supplementary

Answers

Answer:

[tex]\implies[/tex]The answer is Adjacent and Complementary.

Step-by-step explanation:The two corners are complementary and adjacent to each other.So select Adjacent and Complementary.


Given mn, find the value of x
118%

Answers

x=62 bec 180-118=62.

Step-by-step explanation:

180=118-x

180-118=x

x=62

Bill's school is selling tickets to a fall musical.
On the first day of ticket sales the school sold 1 adult ticket
and 6 child tickets for a total of $52.
The school took in $66 on the second day by selling 1 adult
ticket and 8 child tickets.
Find the price of an adult ticket.
•$3
•$10
•$7
•$9

Answers

By solving a system of equations, we can see that the adult ticket costs $10.

How to find the price of the adult ticket?

Let's define the two variables:

x = price of the adult ticket.y = price of the child ticket.

With the given information, we can write a system of equations:

1*x + 6*y = $52

1*x + 8*y = $66

By taking the difference between the two equations we get:

(1*x + 8*y) - (1*x + 6*y) = $66 - $52

2y = $14

y = $14/2 = $7

Now that we know the value of y, we can find the value of x.

Replacing the value of y in the first equation we get:

1*x + 6*$7 = $52

x = $52 - 6*$7 = $10

With this, we know that the adult ticket costs $10.

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Guys can you help me with this FAST!!

Answers

Answer:

1/6

Step-by-step explanation:

30+20= 50

200+100= 300

you divide 50÷300 and you get 1/6

147 divided by 7
(Explanation needed please)

Answers

Answer: 21

Step-by-step explanation:

Use a calculator

21 is going to be your answer

the sum of nine consecutive natural numbers, the first of which is n?

Answers

Answer:

What is the sum equal to?

Step-by-step explanation:

K
What is 0.514 written as a power of 10??

Answers

Answer:

To write this is true scientific notation the decimal point needs to be moved 1 place to the right so the exponent for the 10s term will be negative:

0.514=5.14×10

−1

Answer:5.14

Step-by-step explanation:

The table shows some values of x and y that satisfy the equation y = acosx + b
180

120
150
4 -3V3
-2

0
30
60
10
4 + 3V3
7
Find the value of y when x = 45

X

90
4

Answers

180+ 123=257 thanks again for your help

Please show me how you got the answer. Will give brainliest.

Answers

Answer:          410 possible points

To solve for the possible points in the course, use a proportion and cross multiply.

What is a proportion?

A proportion is two fractions that are equal to each other. For the fractions to be equal, they are proportionate. In our math problem, percentage is proportionate the the number of points.

The fractions represent information you have, and one variable will represent what you are solving for.

Given

Your points = 361

Points to get an 'A' = your points + 8

'A' = 90% of possible points

Find the points needed for an 'A' at 90%

Points to get an 'A' = your points + 8

= 361 + 8

= 369

State variables

let x be the amount of possible points

Write a proportion

We know the number of points for 90% is 369 points. Remember that 90% is the same as 90/100.

Keep the information with the same units inside the same fraction. Here, percentage is represented by the first fraction. Points is represented by the second fraction.

[tex]\displaystyle{\frac{90}{100}=\frac{369}{x}}[/tex]

Solve

We can solve using cross multiplication. This is when we multiply each numerator by the denominator from the other fraction.

[tex]90x = 369*100[/tex]        Simplify by multiplying.

[tex]90x = 36,900[/tex]            Isolate the variable x.

[tex]\displaystyle{\frac{90x}{90} = \frac{36,900}{90}}[/tex]           Divide both sides by 90 to cancel out 90 on the left.

[tex]\displaystyle{x = \frac{36,900}{90}}[/tex]              Divide.

[tex]x = 410[/tex]                    Solved for x, representing the possible points.

∴ The possible points in the art course is 410.

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Answer:

410 possible points

Step-by-step explanation:

(3x-5) + (x+1) = 180

Answers

The value of 'x' for the given expression is calculated as (x = 48).

What is defined as the linear equation in one variable?

A linear equation in one variable is an equation that has only one solution.

It is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. The numbers a' and b' are real numbers.'a' and 'b' are both greater than zero.2x+3=8, for example, is a linear equation with a single variable.

Now, for the given expression;

(3x-5) + (x+1) = 180

Open the brackets.

3x-5 + x+1 = 180

Add the similar parts;

4x - 4 = 180

Further simplifying;

4x = 180 + 4

4x = 184

x = 184/4

x = 48

Therefore, the value of 'x' is estimated as 48.

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( 1/2 x 1/3) x 1/4 = 1/2 x (1/3 x 1/4)
A. Reflexive
B. Commutative
C. Associative
D. Distributive

Answers

Answer:

The answer is commutitve

Which is an illustration of the associative
property?
a. (b.c) = (b.c).a
α · b = α
a (b.c) = (a.b).c
a.b=b.a

Answers

The associative property of multiplication states:

If a, b, and c are ≠ to 0, then a•(b•c)=(a•b)•c

Essentially, it states that the order in which numbers are grouped and multiplied does not matter.

PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!!

Answers

The probability that if 3 donations are made, all 3 of them can be safely used on blood transfusion with someone that has type A will be D. (0.27 + 0.49)³ = 0.4390

How to calculate the probability?

It should be noted that probability simply means the chance that a particular event will occur.

In this case, the probability that if 3 donations are made, all 3 of them can be safely used on blood transfusion with someone that has type A will be:

= (27% + 49%)³

= (0.27 + 0.49)³

= 0.4390

The probability is 0.4390.

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PLEASE HELP!!!!!
A. What is 4.186 rounded to the nearest tenth?
B. What is 2.758 rounded to the nearest tenth?
C. What is 72.05 rounded to the nearest tenth?
D. What is 45.64 rounded to the nearest tenth?
E. What is 82.156 rounded to the nearest tenth?
F. What is 41.31 rounded to the nearest tenth?
G. What is 29.16 rounded to the nearest tenth?
H. What is 17.054 rounded to the nearest tenth?
I. What is 11.65 rounded to the nearest tenth?
J. What is 0.83 rounded to the nearest tenth?
K. What is 29.16 rounded to the nearest tenth?
L. What is 12.48 rounded to the nearest tenth?
M. What is 0.91 rounded to the nearest tenth?
_______________________________________________________
N. What is 20.5 rounded to the nearest whole number?
O. What is 13.71 rounded to the nearest whole number?
P. What is 71.23 rounded to the nearest whole number?
Q. What is 36.57 rounded to the nearest whole number?
R. What is 17.89 rounded to the nearest whole number?
S. What is 50.147 rounded to the nearest whole number?
T. What is 19.05 rounded to the nearest whole number?
U. What is 7.61 rounded to the nearest whole number?
V. What is 92.38 rounded to the nearest whole number?
W. What is 57.25 rounded to the nearest whole number?
X. What is 16.3 rounded to the nearest whole number?
Y. What is 44.08 rounded to the nearest whole number?
Z. What is 17.9 rounded to the nearest whole number?
1. What is 9.06 rounded to the nearest whole number?

Answers

A. 4.2
B. 2.8
C. 72.1
D. 45.6
E. 82.2
F. 41.3
G. 29.2
H. 17.1
I. 11.7
J. 0.8
K. 29.2
L. 12.5
M. 0.9
N. 21
O. 14
P. 71
Q. 37
R. 18
S. 50
T. 19
U. 8
V. 92
W. 57
X. 16
Y. 44
Z. 18

A blueprint of a house shows a dining room wi an area of 7 square inches. If the blueprint' scale is 1 inch : 6 feet, what would be the act area of the dining room? 1​

Answers

The Actual area of the dining room is: 252 square feet.

How to Find the Actual Area Using Scale?

Given that the area of the house on a blue print = 7 square inches.

Scale of the blue print = 1 inch : 6 feet.

Therefore, we would have the following proportion:

Area on blue print/actual area = square of the scale

7/actual area = 1²/6²

7/actual area = 1/36

Actual area = (7)(36)

Actual area = 252 square feet.

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Answer: Actual area (252 square feet).

Explanation:

How to Find the Actual Area Using Scale?

Given that the area of the house on a blueprint = is 7 square inches.

The scale of the blueprint = is 1 inch: 6 feet.

Therefore, we would have the following proportion:

The area on the blueprint/actual area = square of the scale

7/actual area = 1²/6²

7/actual area = 1/36

Actual area = (7)(36)

Actual area = 252 square feet.

Hope it helps!

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 5 large boxes and 2 small boxes has a total weight of 117 kilograms. A delivery of 3 large boxes and 8 small boxes has a total weight of 164 kilograms. How much does each type of box weigh?

Answers

THIS ANSWER WAS DELETED DUE TO NOT BEING TRUE.

II. What are the coordinates
of A' using the rule
(x, y) (x-3, y+7)?
A(2, 5)

Need help

Answers

Answer:

so xtime sy ,fe fwvnvf nfdv bregbrrsikrwnknrhvnk vnf vknvns;;abjwrjkgwnkgwjknnnxnfnfsvmsr

PLEASE GEKO ME EHFND

Answers

Answer: 164 degrees

Step-by-step explanation:

IHG=JHG+IHJ

19x-7=84+7x+17

19x-7=101+7x

12x-7=101

12x=108

x=9

IHG=19x-7

IHG=19(9)-7

IHG=171-7

IHG=164 degrees

If =164 my answer to the question

the inequality always, sometimes, or never true
4x8> 1 + 4(x + 3)

Answers

The given inequality  is never true which means it has no solutions. If an inequality has no actual solution, then there aren't any numbers that might be used to solve it and make the statement true. An inequality can be made true by substituting any real number into it if the solution to the inequality is all real numbers.

Given the expression is 4x ₋ 8 > 1 ₊ 4(x₊3)

first apply the distributive property.

4x ₋ 8 > 1 ₊ 4x ₊ 12

now combine the like terms.

4x ₋ 8 > 4x ₊ 13

Variables should be moved to the equation's left side.

4x ₋ 4x > 13 ₊ 8

combine like terms.

0 > 13 ₊ 8

calculate the sum.

0>21

This is the solution of inequality which has no solutions.

Hence the inequality of the expression is never true.

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Patricia wishes to have a rectangular garden in her backyard. She has 88 ft of fencing with which to enclose her garden. Letting x denote the width of the garden, find a function f in the variable x giving the area of the garden.

Answers

The area of the rectangular garden in terms of a function in x is given by 44x - x²sq. ft.

What is the area of a rectangle?

A rectangle is a closed geometric figure with opposite sides equal to each other. The area of this rectangle is given by the product of its length and width.

Calculating the area of a rectangular garden in terms of a function in x

Let us consider a variable x that denotes the length of a rectangular garden

Given perimeter of a rectangular garden is 88 ft with y as the width of a rectangular garden

Perimeter = 2×(length + breadth)

88 = 2(x + y)

44 = x + y

y = 44 - x

Area of a rectangular garden = xy

= x(44 - x)

= 44x - x² sq. ft

Hence, the area of a rectangular garden in terms of a function in x is given by 44x - x² sq. ft.

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6) What is 1.333... in fraction form?

Answers

Answer:

It would be 1333/1000.

7th-grade question
5. Sara used 4 1/2 packs of pencils in the first 1/4 of the year. At what rate
is Sara using pencils?
A. 1 1/8 packs per year
B. 6 packs per year
C. 16 1/8 packs per year
D. 18 packs per year

Answers

4 1/2 times 4= 18 packs per year


We get 4 above by adding 1/4 four times to complete a period of 1 year.
1/4 + 1/4 +1/4 + 1/4= 1 year

The area of a rectangular garden is 7584 ft squared If the width of the garden is 79 feet, what is its length?

Answers

Length = Area/Width

7584/79 = 96 feet

96 x 79 = 7584 ft²

Answer = 96

Answer: 96

Step-by-step explanation:

Length = Area/Width

7584/79 = 96 feet

96 x 79 = 7584 ft²

Write an equation in slope- intercept form for the line described.
parallel to y = -3x + 4, x- intercept at 4

Answers

Answer:

y = -3x + 12

Step-by-step explanation:

If two lines are parallel, their slopes are equal, then m = -3

x intercept is 4 then y = 0

y = mx + b

0 = -3(4) + b

b = 12

y = -3x + 12

Please help with this question I will give you brainliest

Answers

Answer:

89.50 = 7.75 + 27.25p

subtract 7.75 from both sides

89.50 - 7.75 = 27.25p

81.75 = 27.25p

divide both sides by 27.25

p = 81.75 / 27.25

p = 3

Step-by-step explanation:

The number of people who can go to the amusement park is 3 people

Answer: p=3

Hence, the Linear Equation in two variables is used to determine the total number of people who go to the park is - y=7.75+27.25p

Step-by-step explanation:

89.50=7.75+27.25p

89.50-7.75+27.25p

81.75=27.25

81.75/27.25

p=3

The distance between City A and City B is 2700 miles. On a certain wall​ map, this distance is represented by 9 inches. The actual distance between City C and City D is 4100 miles. How far apart are they on the same​ map?

Answers

The distance between City C and City D is represented by 13.67 inches on a certain wall​ map.

What is Ratio?

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Let x inches would be far apart are they on the same​ map

We can write this as a ratio as

As per the given information,

9 inches : 2700 miles = x inches : 4100 miles

⇒ 9/2700 = x/4100

⇒ x = (4100×9)/2700

⇒ x = 13.67 inches

Therefore, on a certain wall​ map, the distance between City C and City D is represented by 13.67 inches.

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Check all relationships between 1 and 22.

Answers

Answer:

adjacent , linear pair ,

Step-by-step explanation:

and i don't think there is something else

Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original price of $13.50 ​each, but later decreased the price of each by ​$4.00. If they sold all 91 pieces and took in $972.50​, find how many they sold at the original price and how many they sold at the reduced price.

Answers

The number sold at the original price is 27 and they sold 64 at the reduced price.

How to calculate the value?

Let x = number of pieces sold at 13.50

Let y = number of pieces sold at 9.50

The equation will be:

x + y = 91. ..... i

13.50x + 9.50y = 972.50 ..... ii

From equation i x = 91 - y

13.50x + 9.50y = 972.50

13.50(91 - y) + 9.50y = 972.50

1228.50 - 13.50y + 9.50y = 972.50

1228.50 - 4y = 972.50

4y = 1228.50 - 972.50

4y = 256

y = 256/4

y = 64

Since x + y = 91

x = 91 - 64 = 27

Therefore, the number sold at the original price is 27 and they sold 64 at the reduced price.

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Find all integer solutions of each system of inequalities.
a) 6-4b>0
3b-1>0
b) 3-18x<0
0.2-0.1x>0

Answers

Answer:

A: [tex]b < \frac{3}{2}[/tex] and the second equation is: [tex]b > \frac{1}{3}[/tex]

B: [tex]x > \frac{1}{6}[/tex] and the second equation is: [tex]x < 2[/tex]

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Hope this helps!

Have a great day and God bless! :)

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