combinations

Rachel.F · #1 $Old$ November 3rd, 2009, 03:02 PM

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

Plato · #2 $Old$ November 3rd, 2009, 03:43 PM

Quote:

Originally Posted by Rachel.F $View Post$

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 $\sum\limits_{k = 0}^6 \binom{12-k}{k}$