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Laura’s pet bunny, Ghost, hops up a flight of 12 stairs. Ghost can hop up one or two steps at a time, and never hops down. How many ways can Ghost reach the top

  • math -

    number of cases, not worrying about order:

    2hops 1 hop

    6 0
    5 2
    4 4
    3 6
    2 8
    1 10
    0 12

    number of ways each of the above can be arranged

    e.g. the 5 double hops and 2 single hops could be
    dddddss
    sddddds
    etc

    6 0 --- 1
    5 2 -- 7!/(5!2!) = 21
    4 4 -- 8!/(4!4!) = 70
    3 6 -- 9!/(3!6!) = 84
    2 8 -- 10!/(2!8!) = 45
    1 10 -- 11!/10!1! = 11
    0 12 -- 1

    different ways = sum of those = 233

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