SOLUTION: Show all work. A disc jockey has 7 songs to play. Three are slow songs, and four are fast songs. Each song is to be played only once. In how many ways can the disc jockey play th
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Question 424256: Show all work. A disc jockey has 7 songs to play. Three are slow songs, and four are fast songs. Each song is to be played only once. In how many ways can the disc jockey play the 7 songs if
• The songs can be played in any order.
• The first song must be a slow song and the last song must be a slow song.
• The first two songs must be fast songs.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
7 songs to play.
Three are slow songs, and
four are fast songs.
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Each song is to be played only once.
In how many ways can the disc jockey play the 7 songs if
• The songs can be played in any order:::7! = 5040 ways
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• The first song must be a slow song and the last song must be a slow song.
1st song: 3 ways
last song: 2 ways
Middle 5 songs: 5! = 120 ways
Total ways: 3*2*120 720 ways
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• The first two songs must be fast songs.
1st song: 4 ways
2nd song: 3 ways
last 5 songs: 5! = 120
Total ways:4*3*120 = 1440 ways
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Cheers,
Stan H.
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