CA CS CIMA Prakash Somani (Landmark Group) (23502 Points)
19 February 2009Here is one more question on Permutations.
Find the number of ways in which you can climb 10 steps if you can go up 1 or 2 steps at a time.
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CA CS CIMA Prakash Somani
(Landmark Group)
(23502 Points)
Replied 19 February 2009
Here is the answer..(JUST select the below area) at end:
The answer for this question is 89. Solution: Following combination will show the number of 1-step and 2-step jumps needed for completing 10 steps. (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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