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a rabbit climb up a flight of 10 stairs and can only hop 1 or 2 steps each time. he never hops down, only up. How many ways can the rabbit hop up the flight of 10 steps?

  • math -

    First lets look at the number of combinations (order won't matter) to go the 10 steps
    Behind it I will then do the number of permutations

    2 2 2 2 2 ---- 1
    2 2 2 2 1 1 --- 6!/(4!2!) = 15
    2 2 2 1 1 1 1 --- 7!/(3!4!) = 35
    2 2 1 1 1 1 1 1 --- 8!/(2!6!) = 28
    2 1 1 1 1 1 1 1 1 --- 9!/(1!8!) = 9
    1 1 1 1 1 1 1 1 1 1 --- 1

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

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