Question

A disc jockey has to choose three songs for the last few minutes of his evening show. If there are nine songs that he feels are appropriate for that t

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asked 2021-06-14
A disc jockey has to choose three songs for the last few minutes of his evening show. If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?

Answers (1)

2021-06-15
Assuming he doesn't want to repeat any songs, then for the first song, he can choose any of the nine. For the second he can choose any of the nine except the one he played first. So for each of those original nine songs, their are eight options for the second. Thus there are \(\displaystyle{8}×{9}={72}\) ways to play the first two.
One the first two are chosen, there are seven songs from which he can choose for the last. So for each of the 72 options for the first two songs, there are seven options for the last song. Thus there are \(\displaystyle{7}×{8}×{9}={504}\) total ways he could choose and arrange the three songs from the nine.
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