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**1. Homework Statement**

Problem: How many ways are there for 15 boys and 15 girls at a dance to pair up into 15 heterosexual dance couples?

**2. Homework Equations**

This is probably somewhat helpful, but I couldn't figure out exactly how to implement it.

nCr = [tex]\frac{n!}{k!(n-k)}[/tex]

**3. The Attempt at a Solution**

What I thought was if lets say you have all of the boys in a row 1 to 15, and you just rearrange the girls in every possible combination 15! and just match them up with each boy. then I multiply that number by 15 for the boys, and I get a number of like 19615115520000 which seems quite high...

I also tried to do it using a smaller amount of numbers to get an easier idea of how to do it, but it didn't help me much because then the number seemed too small.