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mynameisfunk
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A football team consists of 20 offensive and 20 defensive players. Th 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.
See attachment
motivation: -(4!)2 ways to pair up the players.
-[tex]\frac{40!}{20!(2)^20}[/tex] total ways to pick 20 pairs
-(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
Homework Statement
A football team consists of 20 offensive and 20 defensive players. Th 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.
Homework Equations
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
-(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
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