Question

From a committee consisting of 5 men and 6 women, a sub-committee is formed consisting of 4 men and 3 women. How many different subcommittees are possible?

Answer 1

Answer:  There are 100 different possible subcommittees.

Step-by-step explanation:  We are given that from a  committee consisting of 5 men and 6 women, a sub-committee is formed consisting of 4 men and 3 women.

We are to find the number of possible subcommittees.

The number of ways in which in which 4 men can be chosen from 5 men is given by

$n_1=^5C_4=\dfrac{5!}{4!(5-4)!}=\dfrac{5\times4!}{4!\times1}=5,$

and the number of ways in which 3 women can be chosen from 6 women is given by

$n_2=^6C_3=\dfrac{6!}{3!(6-3)!}=\dfrac{6\times5\times4\times3!}{3\times2\times1\times3!}=20.$

Therefore, the total number of possible subcommittees will be

$n=n_1\times n_2=5\times20=100.$

Thus, there are 100 different possible subcommittees.

Answer 2

Number of combinations of 4 men from 5  =  5

number of combinations of 3 women from 6  = 6C3 =  6*5*4 / 3*2*1 = 20

So there are 5*20 = 100 subcommittees possible.