EXAMPLE 1.5.24

1. The heavy-metal band Death Maggot normally performs 10 songs during a concert. One night, however, they found that they would only have enough time to perform 7 songs, due to the fact that their opening act got called back for three encores. If the band randomly chooses 7 songs to play, how many different outcomes are possible? (All we care about is which 7 songs are chosen.)

2. On the other hand, if they randomly choose 3 songs not to play, how many different outcomes are possible?

3. Assuming that they are only going to play 7 songs from their 10-song repertoire, how many different arrangements are possible?

SOLUTION

1. We are selecting 7 songs from a set of 10 songs. C(10,7) = 120

2. We are selecting 3 songs from a set of 10 songs. C(10,3) =120. Note that the number of ways to choose 3 songs from a set of 10 songs is the same as the number of ways to choose 7 songs from a set of 10 songs.

3. In this case we care not only about which 7 songs are chosen, but also about the order in which the songs are played. P(10,7) = 604,800