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.

MIRB16
Mar 26, 2018

#1**+3 **

I really do not know what this means "Note that identically sized groups are indistinguishable."

BUT

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?

The groups will be MW, MW, MWW

First, How many ways can MWW be chosen 3*4*3

Now how many ways can a MW be chosen for the next group. 2*2

The left overs make the last group.

So I have 3*4*3*2*2 = 144 ways

Melody
Mar 26, 2018

#1**+3 **

Best Answer

I really do not know what this means "Note that identically sized groups are indistinguishable."

BUT

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?

The groups will be MW, MW, MWW

First, How many ways can MWW be chosen 3*4*3

Now how many ways can a MW be chosen for the next group. 2*2

The left overs make the last group.

So I have 3*4*3*2*2 = 144 ways

Melody
Mar 26, 2018