Question

there are 11 women and 9 men in a certain club. if the club is to select a committee of 2 women and 2 men, how many different such committees are possible? 120 720 1,060 1,520 1,980

Answer 1

Correct answer is 1980

Answer 2

Answer:

Number of committees that are possible are 1980

Step-by-step explanation:

Given that,

There are 11 women and 9 men in a certain club.We are required to select 2 men and and 2 women to form a commitee.

We know that,no.of ways of selecting r items out of n items is

$nC_{r}=\frac{n!}{(n-r)!r!}$

No.of ways of selecting 2 men out of 9 men is

$9C_{2}=\frac{9!}{(9-2)!2!} \\ = 36$

No.of ways of selecting 2 women out of 11 women is

$11C_{2}=\frac{11!}{(11-2)!2!} \\ = 55$

Therefore,number of committees that can be formed by 2 men and 2 women is

$36 \times 55 = 1980$

Hence,1980 committees are possible

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