In how many different ways you can climb 10 stairs?

Question

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

Answer 1

10 Stairs can be climbed by -

A. All 10 stairs - 1 at a time
B. 8 stairs - 1 at a time & 2 stairs - 2 at a time
C. 6 stairs - 1 at a time & 4 stairs - 2 at a time
D. 4 stairs - 1 at a time & 6 stairs - 2 at at time
E. 2 stairs - 1 at a time & 8 stairs - 2 at a time
F. All 10 stairs - 2 at a time

A. All 10 stairs - 1 at a time => 1 way
B. 8 stairs - 1 at a time & 2 stairs - 2 at a time => 9C1 ways = 9 ways
C. 6 stairs - 1 at a time & 4 stairs - 2 at a time => 7C1 + 7C2 ways = 28 ways
D. 4 stairs - 1 at a time & 6 stairs - 2 at at time => 5C1 + 5P2 + 5C3 = 35 ways
E. 2 stairs - 1 at a time & 8 stairs - 2 at a time => 5C1 + 5C2 ways = 15 ways
F. All 10 stairs - 2 at a time => 1 way

Total = 89 ways