How many ways can 12 people be divided into 3 equal groups?

[abeen]

The number of ways in which 12 people may be divided into 3 equal groups is_
My ans is 12C4*8C4*4C4=34650.
But my test book contains the answer 5775.
So iam confused. Is my answer correct or am i missing something?

 

[uart]

i missing something?

Just that you are counting all possible orderings of the groups. What I mean is that if you have one particular grouping say { {1 2 3 4} {5 6 7 8} {9 10 11 12} } you are counting that same thing six times over (assuming that the ordering of the groups doesn't matter).

{ {1 2 3 4} {5 6 7 8} {9 10 11 12} }
{ {1 2 3 4} {9 10 11 12} {5 6 7 8} }
{ {5 6 7 8} {1 2 3 4} {9 10 11 12} }
{ {5 6 7 8} {9 10 11 12} {1 2 3 4} }
{ {9 10 11 12} {1 2 3 4} {5 6 7 8} }
{ {9 10 11 12} {5 6 7 8} {1 2 3 4} }

You just need to divide your answer by six (3!) to correct this.

 

[abeen]

Thank you uart.