How many different set lists of 12 songs can the group select to play on tour?
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1. The Cool Gents is a R&B group planning their next concert tour. The band has a total of 25 new songs in their repertoire.
a. How many different set lists of 12 songs can the group select to play on tour? Use permutations or combinations. (Hint: the order of the songs is not relevant.)
b. How many different ways are there for the group to record a CD consisting of 12 songs chosen from 25 new songs? Use permutations or combinations. (Hint: The order in which the songs appear on the CD is relevant).
2. A card is drawn out of a standard deck of 52 cards. Each card can be described by giving its “value” (A, 2,3,4,….10, J, Q, K) and its “suit” (H for hearts, C for clubs, D for diamonds and S for spades). For example, 2S denotes the two of spades and KH denotes the king of hearts. Write out the event described by each of the following statements as a set.
a. E1: “draw a king.”
b. E2: “draw a club.”
c. E3: “draw a face card.” (A “face” card is a jack, queen or king).
3. A card is drawn at random out of a well-shuffled deck of 52 cards. Find the probability of each of the following events. (Do problem #2 first.)
a. E1: “draw a king.”
b. E2: “draw a club.”
c. E3: “draw a face card.” (A “face” card is a jack, queen, or king).
4. An honest coin is tossed three times in a row. Find the probability of each of the following events.
a. E1: “the coin comes up heads exactly twice.”
b. E2: “all three tosses come up the same.”
c. E3: “exactly half of the tosses come up heads.”
d. E4: “the first two tosses come up tails.”
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