1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
avanturin [10]
3 years ago
7

Rework problem 35 from the Chapter 2 review exercises in your text, involving auditioning for a play. For this problem, assume 9

males audition, one of them being Winston, 5 females audition, one of them being Julia, and 6 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available.
Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
6 0

Answer: 1) 6300 ways

2) 2520 ways

3) 0.067

Step-by-step explanation:

For this problem, assume 9 males audition, one of them being Winston, 5 females audition, one of them being Julia, and 6 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available.

How many different ways can these roles be filled from these auditioners?

Available: 9M and  5F and 6C

Cast: 3M and 1F and  2C

As it is not ordered: C₉,₃ * C₅,₁ * C₆,₂

C₉,₃ = 9!/3!.6! = 84

C₅,₁ = 5!/1!.4! = 5

C₆,₂ = 6!/2!.4! = 15

C₉,₃ * C₅,₁ * C₆,₂ = 84.5.15 = 6300

How many different ways can these roles be filled if exactly one of Winston and Julia gets a part?

2 options Winston gets or Julia gets it:

1) Winston gets it but Julia no:

8 male for 2 spots

4 females for 1 spot

6 children for 2 spots

C₈,₂ * C₄,₁ * C₆,₂

C₈,₂ = = 8!/2!.6! = 28

C₄,₁ = 4!/1!.3! = 4

C₆,₂ = 6!/2!.4! = 15

C₈,₂ * C₄,₁ * C₆,₂ = 28.4.15 = 1680

2) Julia gets it but Winston does not

8 male for 3 spots

1 female for 1 spot

6 children for 2 spots

C₈,₃ * C₆,₂

C₈,₃ = 8!/3!.5! = 56

C₆,₂ = 6!/2!.4! = 15

C₉,₃ * C₆,₂ = 56.15 = 840

1) or 2) = 1) + 2) = 1680 + 840 = 2520

What is the probability (if the roles are filled at random) of both Winston and Julia getting a part?

8 male for 2 spots

1 female for 1 spot

6 children for 2 spots

C₈,₂ * C₆,₂

C₈,₂ = = 8!/2!.6! = 28

C₆,₂ = 6!/2!.4! = 15

C₈,₂ * C₆,₂ = 28.15 = 420

p = 420/6300 = 0.067

You might be interested in
`Please solve this extremely easy math problem!
lapo4ka [179]

Answer:

6 cars

Step-by-step explanation:

Simple and fast division.

8 0
3 years ago
Read 2 more answers
I will give brainliest and A LOT OF POINTS please help!!!!!!!!!!!!!!!!!
DedPeter [7]

Answer:

(10,2)(20,4)(30,6)(40,8)

Step-by-step explanation:

In each bracket the first digit divided by the second is equal to 5

10÷2=5

20÷4=5

30÷6=5

40÷8=5

3 0
2 years ago
Mrs. Smith went to the grocery store and bought the fruit below.
lukranit [14]
The answer is 12.69, you just need to put all the groceries together!!
7 0
3 years ago
Please help please !!!!!!!!!!!!!!!
alukav5142 [94]

Answer:

Linear

The function is linear since the graph of it would be a straight line. You can tell this by looking at the equation since there are no squares, roots, division, etc. that would make the line stray.


4 0
3 years ago
The Harris family needs to purchase topsoil for their landscaping project (measuring 50 ft x 40 ft with a thickness of 6 inches
lana66690 [7]
50ft x 40ft x 0.5ft = 1,000 ft³ of soil needed for the project

1000/3= 333.3 bags of soil would be needed, so round up to 334.
334 x $2.25 = $751.50

convert the feet³ to yards³, divide the 1000 ft³ by 27 (27 ft³ in 1 yard³)
1000/27= 37.037(repeating) yd³ I'll round up to 38 yd³
38yd³ x $18 = $684 + $50 delivery fee = $734

So, the bulk soil is less expensive by $17.50
7 0
3 years ago
Other questions:
  • Garret is in the middle of a 20 -minute bike ride. It takes 4 minutes for him to go a kilometer, so he'll end up going 5 kilomet
    13·1 answer
  • On a certain island there are two populations of deer. after t years the numbers of deer in the two populations are p(t)=100et a
    5·1 answer
  • I don't inderstand how would i graph and find the range and domain
    11·1 answer
  • What is the length of ab
    6·1 answer
  • Help on my geometry plzzzz
    12·1 answer
  • What are three different ways to make the number 15,638 with only hundreds, tens, and ones?
    8·2 answers
  • X- 0.1x + 2.70 = 56.70 solve for the answer
    8·1 answer
  • Please answer this question with how do work it out?
    14·1 answer
  • Evaluate the expression: 6(a + b) where a = -3 and b = 6
    14·1 answer
  • Find the value of sin E rounded to the nearest hundredth, if necessary.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!