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There are 32 teams in the NFL. Sixteen of the teams are in the American Football Conference (AFL) and the other 16 teams are in the National Football Conference (NFC). At the beginning of the season, Julia tried to predict the teams that would be in each conference's championship by randomly drawing 4 teams (2 AFC teams and 2 NFC teams) from a hat. What is the probabliliy that the 4 teams she selected are the same 4 teams that will be in the conferences' championships? Express your answer as a common fraction.

This doesn't make any sense! Please explain!

  • MATH -

    same question posted by Kate

  • MATH -

    i still don't understand how you got that

  • MATH -

    To do these kind of problems, you must have studied the difference between permutations and combinations.
    This is a a "combination" type question
    You are choosing 2 out of 16 different items in the AFL
    that would be C(16,2) = 16!/(14!2!) = 120
    You have the same situtation for the other league.
    so the number of ways to choose 2 teams from AFL, and 2 teams from NFC
    = 120*120=14400
    But obviously only one of these will be the correct final selection.
    so prob = 1/14400

    I really don't know how to explain it in any other way.

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