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March 25, 2017

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a rabbit can climb one or two steps at a time on a ten step staircase, but he never goes back down. In how many different ways can the rabbit climb a flight of ten steps

  • 8th grade - ,

    5 2's -- one way
    4 2's 2 1's ---- number of ways = 6!/(4!2!) = 15
    (e.g. 222211, 11222, 212122, etc )

    3 2's 4 1's ---- number of ways = 7!/(4!3!) = 35
    2 2's 6 1's ---- number of ways = 8!/(2!6!) = 28
    1 2 8 1's ---- number of ways = 9!/(1!8!) = 9
    all 1's ---- one way

    total 1+15+35+28+9+1 = 89

    Wow for grade 8!!!

  • 8th grade - ,

    89

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