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Ryan reaches into his gym bag for a pair of running shoes. If there are seven different pairs of shoes loose in the bag, how many ways can he pick two shoes that do not match?

  • math -

    combinations of 14 things two at a time = 14!/[12!(2!)]=14*13/2 = 7*13 = 91
    but some of those are matching, namely 7 pairs, so there are 91-7 = 84 ways

  • math -

    Why did you divide the answer from 14*13 by 2?

  • math -

    23! = 2*1 = 2

  • math -

    excuse typo
    2! = 2*1 = 2

  • math -

    combinations is
    n!/[ (n-r)! r! ]
    here n=14
    r = 2

  • math -

    14! = 14*13*12 * 11 etc
    12! =12*11 etc
    so
    14!/12! = 14 * 13
    now divide that by 2! which is 2

  • math -

    what I did is
    Total= 14*13=182
    Matched pairs=7*2=14
    182-14- 168 possibilities

  • math -

    but you can not tell left-right
    from
    right-left

  • math -

    well for the matched pairs part the 7 is the pairs and the 2 is the orders of pairs LR and RL

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