1. C(N, k)

(a) Find the number of 8-letter words with 3Rs and 5Ls using the C(N,k) formula, but do it by hand, i.e. write out all the numbers in the formula and simplify. [Doing this by hand illustrates how the formula really works.]

(b) Now let's see why it's so useful to have a formula for C(N, k): Find the number of 15-step paths with 11 rights and 4 lefts.

Feel free to use an online C(N,k) calculator, such ashttps://www.desmos.com/scientific (click on "func", then on "nCr", then enter the value of N, then a comma, then the value of k, inside the parentheses).