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Question

If N is the number of ways in which a person can walk up a stairway which has 7 steps if he can take 1 or 2 steps up the stairs at a time, then the value of N/3 is

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Solution

x denotes the number of times he takes unit step and y denotes the number of times he takes 2 steps, then x+2y=7,
Then we must have x=1,3,5,7
If x=1, the steps will be 1,2,2,2
number of ways =4!3!=4

If x=3 the steps will be 1,1,1,2,2
number of ways =5!2!3!=10

If x=5 the steps will be 1,1,1,1,1,2
number of ways 6C1=6

If x=7 the steps will be 1,1,1,1,1,1,1,1
number of ways 7C0=1
Hence total number of ways =N=21
N/3=7

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