Stressful Auditions

Probability Level 3

A play has two male roles, two female roles, and two roles that can be either gender. Only a man can be assigned to a male role, and only a woman can be assigned to a female role. If five men and six women audition, what are the last three digits of the number of ways the six roles can be assigned?


The answer is 200.

Finn Hulse by Finn Hulse , 21, USA

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2 solutions

Tejashwi Kumar
Apr 7, 2014

C(5, 2) 2! *C(6, 2) 2! C(7, 2) 2! (assuming roles to be different) hence last three digits is 200

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Finn Hulse
Feb 18, 2014

Let's start with the male roles. Because the two men are distinct AND THE ROLES ARE, there are NOT 5 choose 2 ways choose the men. There are 5 × 4 5 \times 4 . For the female, there are 6 × 5 6 \times 5 ways, and because there will be 7 people left over for the other 2 roles, there are 7 × 6 7 \times 6 ways to choose that. Multiplying all numbers together get 25,200, the last 3 digits of which are 200.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

It is not explicit that the roles are distinct.

Calvin Lin Staff - 7 years, 2 months ago

yes its not specified anywhere that the roles are distinct............ if you assume the roles to be the same there should be 3150 ways of assigning the roles........

Mayankk Bhagat - 7 years, 2 months ago

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