Twenty different books are to be put on five book shelves, each of which holds at Least twenty books. (a) How many different arrangements are there if you only care about the number of books on the shelves (and not which book is where)? (b) How many different arrangements are there if you care about I which books are where but the order of the books on the shelves doesn't matter? Suppose a poker hand contains seven cards rather than 5. Compute the probabilities of the following poker hands: (a) a seven-card straight (b) Four cards of one rank and three of a different rank. (c) Seven cards each of different rank.