Let us assume a person climbing the stairs can take one stair or two stairs at…

Answer: 34

Reasoning using recurrence:

1. Let ways(n) be the number of ways to climb n stairs when you can take 1 or 2 steps at a time. For n>2, any valid sequence either starts with a single step (then there are ways(n-1) ways for the rest) or starts with a double step (then there are ways(n-2) ways for the rest). So:

   ways(n) = ways(n-1) + ways(n-2)

2. Base values: ways(1) = 1 (only one single step), ways(2) = 2 (either two singles or one double).

3. Compute up to n = 8 using the recurrence:

   ways(1)=1, ways(2)=2, ways(3)=3, ways(4)=5, ways(5)=8, ways(6)=13, ways(7)=21, ways(8)=34

Combinatorial check (alternate method):

• If there are 0 double steps, all 8 are single steps: C(8,0) = 1 way.

• If there is 1 double step, there are 7 moves in total and choose its position: C(7,1) = 7 ways.

• If there are 2 double steps, there are 6 moves total: C(6,2) = 15 ways.

• If there are 3 double steps, there are 5 moves total: C(5,3) = 10 ways.

• If there are 4 double steps, there are 4 moves total: C(4,4) = 1 way.

Summing these counts: 1 + 7 + 15 + 10 + 1 = 34, confirming the recurrence result.