Question

The library steps: There are 10 steps leading up to the library entrance. You walk up the stairs
taking 1 step at a time, 2 steps at a time, or some combination of 1 and 2 steps. How many ways
are there to go up the steps?

Answer 1

ok?

Answer 2

All steps one at a time: 1 way

Two steps once, the other 8 one at a time: 211111111, 121111111, etc c(9, 1) = 9 ways

Two steps twice, the other 6 one at a time: 22111111, 21211111, etc c(8, 2) = 28 ways

Two steps 3 times, one step 4 times: c(7, 3) = 35 ways

Two steps 4 times, one step 2 times: c(6, 4) = 15 ways

Two steps 5 times: one way

Overall: 1 + 15 + 35 + 28 + 9 + 1 = 89 ways