Question 366801: 5. Show all work. A disc jockey has 10 songs to play. Seven are slow songs, and three are fast songs. Each song is to be played only once. In how many ways can the disc jockey play the 10 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 Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A disc jockey has 10 songs to play. Seven are slow songs, and three are fast songs. Each song is to be played only once. In how many ways can the disc jockey play the 10 songs if
* The songs can be played in any order.
The 1st is 1 of 10, then 1 of 9, 8, 7 etc
= 10*9*8*7... = 10!
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* The first song must be a slow song and the last song must be a slow song.
The 1st is 1/7, the last is 1/6. The other 8 are 1 of 8, 7, 6, 5, 4, 3, 2, 1
= 7*6*(8!)
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* The first two songs must be fast songs
3*2*(8!)
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