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At Maryland Middle School, there are 9 mathematics classes. If two mathematics classes are selected for a school competition, what is the number of possible outcomes?

  • math -

    combinations of 2 out of 9

    C(n,r) = n!/[(n-r)! (r!) ]
    = 9! /[ 7! * 2! ]

    = 9*8 *7! / [ 7! * 2]
    =9*4
    = 36

  • math -

    Or use Pascal's triangle
    row 9 is
    1 9 36 84 126 126 84 36 9 1

    so r = 0 --> 1
    r = 1 = 9 of course
    r = 2 = 36

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