Kenneth Rosen Edition 7 Exercise 6.3 Question 34 (Page No. 414)

Question

Suppose that a department contains $10$ men and $15$ women. How many ways are there to form a committee with six members if it must have more women than men?

Answer 1

Such a committee can be formed wither by

0 men and 6 women,

1 men and 5 women,

2 men and 4 women.

There are C(10, 0) ·*C(15, 6) + C(10, 1) * C(15, 5) + C(10, 2) *C(15, 4)

=[ (10! /0!10!) * (15!/ 6!9! ) ]+ [(10!/ 1!9!) * (15! /5!10!)] + [( 10! /2!8! )* (15! /4!11! )]

= 96460