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

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.

Answer 2

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=(5!)/(4!(5-4)!)=(5*4!)/(4!*1)=5,`

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

`n_2=^6C_3=(6!)/(3!(6-3)!)=(6*5*4*3!)/(3*2*1*3!)=20.`

Therefore, the total number of possible subcommittees will be

`n=n_1* n_2=5*20=100.`

Thus, there are 100 different possible subcommittees.