+0  
 
+1
66
9
avatar+399 

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.

 Oct 8, 2020
 #2
avatar
+1

    MW      WM     MWW

I don't see any other option.

Stupid questioncheeky

 Oct 9, 2020
 #3
avatar+111124 
+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

 Oct 10, 2020
edited by Melody  Oct 10, 2020
edited by Melody  Oct 10, 2020
 #4
avatar
+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.

 Oct 10, 2020
 #5
avatar+111124 
+1

Yes but we have assumed that individuals do not matter.

Our answers assume only gender matters.

 

If individuals also matter then

I think

4C2*3  *  2  =  4*3*2 = 24 is the answer.

Melody  Oct 10, 2020
 #6
avatar+399 
0

That's wrong sad

 Oct 11, 2020
edited by HelpBot  Oct 11, 2020
 #7
avatar+111124 
0

Maybe so but you are expected to give your reason and to be polite about it.

Melody  Oct 11, 2020
 #8
avatar+399 
+2

Srry. It's wrong because the answer key says it's 3 times 6 times 2 which is 36.

 

C(3 1) is three and C(4 2) is 6 so 3 times 6 times 2 (two ways to pair up the men and women left)

 

It's fine at least I got it now :-)

 Oct 12, 2020
 #9
avatar+111124 
+1

You are right.

 

My answer   4C2*3  *  2    was correct but my simplification of it had a careless error

 

4C2=6 (not 4)

 

6*3*2= 36  

Melody  Oct 12, 2020

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