MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

Answer: 1) 6300 ways2) 2520 ways3) 0.067Step-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 Β 5F and 6CCast: 3M and 1F and Β 2CAs it is not ordered: Cβ,β * Cβ
,β * Cβ,β Cβ,β = 9!/3!.6! = 84Cβ
,β = 5!/1!.4! = 5Cβ,β = 6!/2!.4! = 15Cβ,β * Cβ
,β * Cβ,β = 84.5.15 = 6300How 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 spots4 females for 1 spot6 children for 2 spotsCβ,β * Cβ,β * Cβ,β Cβ,β = = 8!/2!.6! = 28Cβ,β = 4!/1!.3! = 4Cβ,β = 6!/2!.4! = 15Cβ,β * Cβ,β * Cβ,β = 28.4.15 = 16802) Julia gets it but Winston does not8 male for 3 spots1 female for 1 spot6 children for 2 spotsCβ,β * Cβ,β Cβ,β = 8!/3!.5! = 56Cβ,β = 6!/2!.4! = 15Cβ,β * Cβ,β = 56.15 = 8401) or 2) = 1) + 2) = 1680 + 840 = 2520What is the probability (if the roles are filled at random) of both Winston and Julia getting a part?8 male for 2 spots1 female for 1 spot6 children for 2 spotsCβ,β * Cβ,β Cβ,β = = 8!/2!.6! = 28Cβ,β = 6!/2!.4! = 15Cβ,β * Cβ,β = 28.15 = 420p = 420/6300 = 0.067