Number of ways to climb 11 stairs if you can climb 1 or 2 stairs every time

Hi,

I have a math unit test on combinatorics and I couldn't solve this problem. Please help!

Thanks in advance

Re: Number of ways to climb 11 stairs if you can climb 1 or 2 stairs every time

Quote:

Originally Posted by

**verasi** I have a math unit test on combinatorics and I couldn't solve this problem. Please help!

Here are the possibles:

$\displaystyle \begin{array}{*{20}{c}}5&{twos}&{}&1&{one}\\4&{two s}&{}&3&{ones}\\3&{twos}&{}&5&{ones}\\2&{twos}&{}& 7&{ones}\\1&{two}&{}&9&{ones}\\0&{twos}&{}&{11}&{o nes}\end{array}$

For example, we can arrange 4 twos and 3 ones in $\displaystyle \frac{7!}{4!\cdot 3!}$ ways.

Now you do each and add.