*For the following scenario, state whether it involves a permutation or a combination, then find the number of possibilities. The batting order for nine players on a 12 person team.

Explain why “the sum of xand y” is the same as “the sum of yand x,” but “the difference of xand y” is not the same as “the difference of yand x.” Try substituting two random numbers for x and yto help you explain.

In horse racing, a “trifecta” occurs when a bettor wins by selecting the first three finishers in the exact order (1 St place, 2nd place, and 3rd place). How many different trifectas are possible if there are 14 horses in a race?

Over the past year, John has purchased 30 books. In how many ways can he pick four of these books and arrange them, in order, on his nightstand bookshelf? In how many ways can he choose four of these books to take with him on his vacation at the shore?