In how many different ways can 3 men and 4 women be placed into two groups of two people and one group of three people if there must be at least one man and one woman in each group? Note that identically sized groups are indistinguishable.

HelpBot Oct 8, 2020

#3**+1 **

In how many different ways can 3 men and 4 women be placed into two groups of two people and one group of three people if there must be at least one man and one woman in each group? Note that identically sized groups are indistinguishable.

If you only care about gender

~~FFF MM MWF ~~

~~MFF MM FF~~

**MFF MF MF**

~~MMF MF FF~~

~~MMM FF FF~~

So I get 1 ways

Melody Oct 10, 2020

#4**+1 **

Take one of the MF groups.

Are there not 12 ways in which that can be set up ?

Any one of three of the men with any one of the four women.

Guest Oct 10, 2020