Climbing n stairs 1 or 2 at a time; count ways to climb stairs.

abhimahatu

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[FONT=&quot]There are n stairs, a person standing at the bottom wants to reach the top. The person can climb either 1 stair or 2 stairs at a time. Count the number of ways, the person can reach the top.

I know a way to solve this by making a recurrence relation. Is there any way to solve this using permutations and combination?[/FONT]
 
There are n stairs, a person standing at the bottom wants to reach the top. The person can climb either 1 stair or 2 stairs at a time. Count the number of ways, the person can reach the top.

I know a way to solve this by making a recurrence relation. Is there any way to solve this using permutations and combination?
There are loads of discussions of the Fibonacci-based recurrence relation (such as here, here, and here). Closed-form is harder to find, and is based on converting the Fibonacci-based terms into closed form, such as is shown here. ;)
 
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