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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