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I am trying to figure out how many combinations you can get if $8$ boys are paired up with $8$ girls.

I was thinking it could possibly be something like $8!$ or $8! \cdot 8!$. Something with factorials but I'm not sure.

N. F. Taussig
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    "factories"? Or do you mean "factorials"? – amWhy Dec 06 '17 at 01:02
  • Hahaha autocorrect because I'm on my phone my apologies –  Dec 06 '17 at 01:03
  • Hint: The first boy can be paired with 8 girls, the second with 7, the third with 6,... – eepperly16 Dec 06 '17 at 01:04
  • Spot on with your intuition/thought that it is a straight factiorial, 8! What confused you, or made you second guess the correct answer you found? That's okay to second guess oneself; everyone does it at one time or another. – amWhy Dec 06 '17 at 01:08
  • I was basically pretty sure that 8! Was involved but I was second guessing whether i needed to do 8! * 8! One for each boy and girl or just one all together –  Dec 06 '17 at 01:09
  • Well you did good with what you were pretty sure about. – amWhy Dec 06 '17 at 01:10

1 Answers1

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First of all, it's "Factorial" not "Factories". For the first boy, there are $8$ girls that can match him. For the second boy, there are $7$ girls that can match him. We keep applying this until we get $8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1 = 40320$.

The answer is $\boxed{40320}$

A Piercing Arrow
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