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Decide whether the situation described involves a permutation or a combination of objects. (a) a telephone number (b) a Social Security number (c) a hand of cards in poker (d) a committee of politicians (e) the "combination" on a padlock (f) an automobile license plate (g) a lottery choice of six numbers where order does not matter

Solve each problem. Suppose that each of the \(n(\) for \(n \geq 2)\) people in a room shakes hands with everyone else, but not with himself or herself. Show that the number of handshakes is \(\frac{n^{2}-n}{2}\)

A menu offers a choice of 3 salads, 8 main dishes, and 5 desserts. How many different 3 -course meals (salad, main dish, dessert) are possible?

How many 7 -digit telephone numbers are possible if the first digit cannot be 0 and (a) only odd digits may be used? (b) the telephone number must be a multiple of 10 (that is, it must end in 0 )? (c) the telephone number must be a multiple of \(100 ?\) (d) the first 3 digits are \(481 ?\) (e) no repetitions are allowed?

In an experiment on social interaction, 9 people will sit in 9 seats in a row. In how many ways can this be done?

In a club with 15 members, in how many ways can a slate of 3 officers consisting of president, vice-president, and secretary/treasurer be chosen?

A baseball team has 20 players. How many 9-player batting orders are possible?

In how many ways can 5 players be assigned to the 5 positions on a basketball team, assuming that any player can play any position? In how many ways can 10 players be assigned to the 5 positions?

If a bag contains 15 marbles, how many samples of 2 marbles can be drawn from it? How many samples of 4 marbles can be drawn?

A city council is composed of 5 liberals and 4 conservatives. Three members are to be selected randomly as delegates to an urban convention. (a) How many delegations are possible? (b) How many delegations could have all liberals? (c) How many delegations could have 2 liberals and 1 conservative? (d) If 1 member of the council serves as mayor, how many delegations are possible that include the mayor?