Climbing 10 Steps - Puzzle for CPT

(10,0) (8,1) (6,2) (4,3) (2,4) (0,5)

Now the question is, "For each of these possibilities, how many ways

can the different steps be arranged?".

Lets take the first one (10,0). Here only one way to complete the 10 steps.

Next (8,1). Here you can get 9 ways to complete the 10 steps.

The nine ways are as follows...

(2,1,1,1,1,1,1,1,1)

(1,2,1,1,1,1,1,1,1)

(1,1,2,1,1,1,1,1,1)

(1,1,1,2,1,1,1,1,1)

(1,1,1,1,2,1,1,1,1)

(1,1,1,1,1,2,1,1,1)

(1,1,1,1,1,1,2,1,1)

(1,1,1,1,1,1,1,2,1)

(1,1,1,1,1,1,1,1,2)

Like these ways we get the number of way from the following combination.

(6,2) - we can get 28 ways.

(4,3) - we can get 35 ways.

(2,4) - we can get 15 ways.

(0,5) - we can get 1 way.

So the total number of ways to climbing 10 steps is.

1+9+28+35+15+1 = 89.

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