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Neel climbs a staircase of 6 steps, taking either 1 step or 2 steps at a time. In how many different ways can he reach the top?

Competition practicePermutations & Combinations

A21
B13
C8
D12

Step-by-Step Solution

Count by the number of 2-steps

k : k = 0

: 1 way;

k = 1

: 5 moves, choose the 2-step,

^{5} C_{1} = 5

;

k = 2 :^{4} C_{2} = 6

;

k = 3

: 1. Total

1 + 5 + 6 + 1 = 13

.

Answer: B) 13

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