(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A football team consists of 20 offensive and 20 defensive players. The players are to be paired to form roommates. They are paired at random. What is the probability that there are exactly 4 offensive/defensive pairs.

2. Relevant equations

3. The attempt at a solution

See attachment

motivation:

-(4!)^{2}ways to pair up the players.

-[tex]\frac{40!}{20!(2)^20}[/tex] total ways to pick 20 pairs (that is a 2^20 where my graphic messed up)

-(20 choose 4)^{2}ways to pick the 4 players to be paired up

-[tex]\frac{32!}{16!(2)^16}[/tex] ways to pair up the rest of the guys (that is a 2^16 where my graphic messed up)

What confuses me is the pairing up of the players of the offensive/defensive pairs. Should it be 4! or 4!^{2}? Otherwise I think the solution is good?

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# Probability problem (counting)

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