There are 119 Division 1A college football teams: 1) How many Top 25 rankings are possible? 2) How many ways are there to choose eight teams and seed them (1 through 8) for a playoff? 3) How many ways are there to choose eight
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Anonymous
ANSWERS: 2
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The number of combinations of 119 teams taken 25 at a time is the binomial coefficient C(119,25) = = 119!/(94!25!) = (119*118*...*95)/25! = about 3.3*10^25. The rest of your question is unclear.
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Assuming order matters for the first question, you can pick any of the 119 teams for the first spot in the polls, then any of the remaining 118 for the second spot, and so on. So 119*118*...*96*95 rankings are possible, which is conveniently expressed as 119!/94! = P(119,25). If order doesn't matter, it's the answer above (C(119,25)=119!/(25!94!)) Question 2 can be answered similarly: 119*118*...*113*112 = 119!/111! = P(119,8) And (3) 119!/(8!111!) = C(119,8)
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