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A group of nine people is be split into three teams, so that one team has four people, another team has four people, and the final team has one person. How many ways can this be done?

 Nov 27, 2020
 #1
avatar+112531 
+1

I think that there are 9 ways to chose the 1

then there are 8C4 ways to choose 4.  

But each time you choose 4 you are also choosing the other 4 in the last group so my best guess is

 

9* 8C4 divided by 2

=9* 70 /2   

= 315 ways.

 Nov 27, 2020
 #2
avatar
+1

MAYBE this?

 

choose 4 people from the 9      9 C 4 = 126

  now choose 4 people from the remaining 5    5 C 4 = 5

    and there is one left

126 x 5 x 1 = 630 ways

 Nov 27, 2020
 #3
avatar+112531 
+1

You have doubled counted.

Say the people are

A,B,C,D,E,F,G,H,J

 

Say you chose J as the single person then you chose  A,B,C,D for the first group and then you are left with E,F,G,H for the last group.

this is the same as

............Chose J as the single person then you chose  E,F,G,H for the first group and then you are left with A,B,C,D  for the last group.

 

I am pretty sure my answer is correct.

Melody  Nov 27, 2020

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