Posted by rob on Tuesday, January 26, 2010 at 10:40pm.
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  Reiny, Tuesday, January 26, 2010 at 11:02pm
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  fay, Thursday, October 13, 2011 at 11:25am
89
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