Number of ways to take 32 steps??

Anniekinnz said:

Consider a stairway with 30 steps, you are now on the 3^rd step.Calculate how many ways you can take 32 steps if you can either go forward or backward in each step.Make sure you do not leave the stairway at any point.

help!!!

Click to expand...

Start counting - you can go 1 step up and one step down - for 16 times.

Or 4 steps up and 4 steps down - 4 times,

or go up 4 steps then 1 step up and one step down for 14 times

and so on...

Now think about it - is there a pattern in these counting - can we use permutation combination with these?

Please share your work, with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

If 30 stairs and 32 steps is too much to consider, can you do the problem with a small number of stairs and steps?