Assume that you have a committee of 14 members, made up of 7 men and 7 women.

Question

the rest of my question: In how many ways can the 3 tasks be assigned so that both men and women are given assignments?

Answer 1

you have 7 men and 7 women

you have 3 tasks

2 women and 1 man can do the tasks, or, 2 men and 1 woman can do the tasks

2 women and 1 man...

how many ways can you select 2 women from 7 women ?

7!/2!(7-2)!=7!/2!5!=7*6/2=21 ways

each group of 2 women can be paired with 1 of 7 men

21*7=147 ways

2 men and 1 woman...

the math is the same because you have 7 men and 7 women

21 ways to group the men by 2s

each group of 2 men can be paired with 1 of 7 women

21*7=147 ways

147+147=294 ways