Discussion: In this problem the student gives a very sophisticated treatment. Rather than doing special numerical cases, the student recognizes that the number of paths is the same as the number of ways of chosing 4 up from amongst 10.

Written response:Great observation. It is typical for beginning problem solvers to recursively put the number of paths to each and begin to see that they are the numbers that occur in Pascal's triangle and then prove the result by induction. Yours is the experienced/sophisticated way of doing it.