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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 ?

+1 vote
posted May 14, 2015 by Ankit Kamboj

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1 Solution

+2 votes

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

solution May 14, 2015 by Salil Agrawal
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 .
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.
I am glad to be of help :)

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