In how many different ways can 3 men and 4 women be placed into one group of three people and one group of four people if there must be at least one man and one woman in each group?

Guest Jul 4, 2022

#1**+1 **

Here's my approach to this one

We only need to consider the group of three.......the other group of 4 will meet our requirement automatically

Case 1 - 2 men and 1 woman in the group of 3

We have the choice of (3 men x 2 men x 4 women) = 24 groups

Case 2 - 1 man and 2 women in the group of 3

We have the choice of (3 men x 4 women x 3 women ) = 36 groups

So

24 + 36 = 60 ways

CPhill Jul 4, 2022