algebra

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Find the number of ways the top four can finish in a race of nine people.

  • algebra -

    Assuming order matters, i.e.
    A,B,C,D is counted differently as B,A,C,D.

    There are 9 choices for the first place, 8 places for the second, 7 places for the third, and 6 places for the fourth. Applying the multiplication rule, there are 9*8*7*6 ways, or
    P(9,4) [permutations]
    =9!/(9-4)!

    If order does not matter, the above must be divided by 4! combinations among the top four, or
    number of ways
    =C(9,4)
    =9!/[(9-4]!4!]

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