Question

A committee of 6 people is chosen from 9 women and 9 men How many differentcommittees are possible that consist of 3 women and 3 men?

Answer 1

There are 7,056 different committees that consist of 3 women and 3 men.

Step-by-step explanation:

In order to find the number of different committees that consist of 3 women and 3 men, we need to consider the combinations that can be formed from the available options. There are 9 women to choose from, and we need to select 3 of them. This can be done in C(9, 3) ways. Similarly, there are 9 men to choose from, and we need to select 3 of them, which can be done in C(9, 3) ways as well. Since the selection of women and men are independent of each other, we can multiply the two combinations together to find the total number of different committees.

C(9, 3) * C(9, 3) = (9! / (3! * (9-3)!)) * (9! / (3! * (9-3)!))

= (9*8*7)/(3*2*1) * (9*8*7)/(3*2*1)

= 84 * 84

= 7056

Answer 2

A committee of 6 people is chosen from 9 women and 9 men How many different

committees are possible that consist of 3 women and 3 men?

we have that

The formula for combinations is

`C=n!/\mleft[\mleft(n-r\mright)!*r!\mright]`

where

n is the total number of objects you choose from

r is the number that you choose to arrange

step 1

9 women choose 3

n=9

r=3

substitute