math
posted by kC .
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?

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 
32 times