How many ways can you go up a 10 step staircase if you have very long legs and make 1, 2, OR 3 step moves?
+118608 How many ways can you go up a 10 step staircase if you have very long legs and make 1, 2, OR 3 step moves?''
Lets see
3 3 3 1 4 permutations
3 3 2 2 4!/(2!2!) 6 permutations
3 3 2 1 1 5!/(2!2!) = 30 permutatiions
3 3 1 1 1 1 6!/(2!4!) = 15 permutations
3 2 2 2 1 5!/(3!) = 20 permutations
3 2 2 1 1 1 6!/(2!3!) = 60 permutations
3 2 1 1 1 1 1 7!/(5!) = 42 permutations
3 1 1 1 1 1 1 1 8!/7! = 8 permutations
2 2 2 2 2 1 permutation
2 2 2 2 1 1 6!/(4!2!) = 15 permutations
2 2 2 1 1 1 1 7!/(3!4!)= 35 permutations
2 2 1 1 1 1 1 1 8!/(2!6!)= 28 permutations
2 1 1 1 1 1 1 1 1 9!/(8!) = 9 permutations
1 1 1 1 1 1 1 1 1 1 1 permutation
4+6+30+15+20+60+42+8+1+15+35+28+9+1 = 274
I get 274 
