Answer each of the following.

a. Find the probability of selecting the five winning numbers from 1, 2, ... , 31.

b. The Wisconsin Badger 5 lottery is won by selecting the correct five numbers from 1, 2, ... , 31. What is the probability of winning if the rules are changed so that in addition to selecting the correct five numbers, you must now select them in the same order as they are drawn?

Find the probability of winning the indicated lottery by buying one ticket. In each case, numbers selected are different and order does not matter. Express the result as a fraction.