A staircase has 10 steps , you can walk up taking one or two steps at a time . how many ways can go up to top of stair ?

Question

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

Answer 1

10C0 + 9C1 + 8C2 + 7C3 + 6C4 + 5C5
= 1+9+28+35+15+1
= 89

Comments

Sir , i didn't got your solution ,
my solution is of fibonacci series , like for 1step ==1 , 2nd step 1+1 or 2 ==2ways , 3rd step  1+1+1 or 1+2 or 2+1 ==3ways , so ,1,2,3,5,8,13,21,34,55,89 ,  for 10th step 89 ways .

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I just tried for two three numbers and saw this logic is arriving (not sure why), but fibonacci  series is more logical :) thanks for asking great puzzle.

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I am glad to be of help :)