# Math Help - combinations

1. ## combinations

we want to up stairs with 12 steps. We can pass by to steps on once. How many ways can we up the stairs?
Solution: 233

Please help. I had already done but i didnt get the correct answer, only aproximations

2. Originally Posted by Rachel.F
we want to up stairs with 12 steps. We can pass by to steps on once. How many ways can we up the stairs?
Solution: 233
We can decide to use anywhere from zero to six double steps (two at a time).
For example: we decide to take 3 double steps: three 2’s and six 1’s.
The number of ways we can do that is $\frac{9!}{3!\cdot 6!}=\binom{9}{3}$.
So calculate $\sum\limits_{k = 0}^6 \binom{12-k}{k}$