# Prom Possibilities

• Feb 28th 2007, 01:39 PM
Mr_Green
Prom Possibilities
9 boys and 6 girls are going to prom together. How many different ways are there to arrange them into six boy-girl couples? (Assume the remaining three boys don't mind going stag.)

Thanks
• Feb 28th 2007, 01:55 PM
Aryth
Quote:

Originally Posted by Mr_Green
9 boys and 6 girls are going to prom together. How many different ways are there to arrange them into six boy-girl couples? (Assume the remaining three boys don't mind going stag.)

Thanks

Pairing 6 boys with three girls is represented by the following Combinations with the format nCr:

15C6 x 15C6 = 3003^2 = 9,018,009 ways to arrange six boy-girl couples.
• Feb 28th 2007, 02:37 PM
Mr_Green
wow. that's a lot of possibilities..aha
• Feb 28th 2007, 02:49 PM
Plato
Quote:

Originally Posted by Mr_Green
wow. that's a lot of possibilities..aha

In fact, it is too many! It is a gross overcounting.
This is a permutation of nine choosing 6: P(9,6)=60480.

Suppose we have the girls: Ann, Bee, Cat, Dot, Eliz, and Fran.
We have 9 choices for Ann; 8 choices for Bee; 7 choices for Cat, …, 4 choices for Fran.