Question 673995: A disc jockey has 9 songs to play. Five are slow songs, and 4 are fast songs. Each song is to be played only once. In how many ways can the disc jockey play the 9 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.
Can you please explain this as you go. I not just out for an easy answer, I need insturction.PLEASE
Found 2 solutions by stanbon, chandrumail:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A disc jockey has 9 songs to play. Five are slow songs, and 4 are fast songs. Each song is to be played only once. In how many ways can the disc jockey play the 9 songs if
The songs can be played in any order.
There are 9 songs.
1st song can be one of 9
2nd song can be one of 8
3rd song can be one of 7
etc.
Ans 9! = 362,880 ways
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The first song must be a slow song and the last song must be a slow song.
1st song can be one of 5
Last song can be one of 4
Middle 7 songs can be in 7! = 5040 ways
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Ans: 5*4*5040 = 100,800 ways
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The first two songs must be fast songs.
Ans: 4*3*7! = 12*5040 = 60,480 ways
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Cheers,
Stan H.
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Answer by chandrumail(4) (Show Source):
You can put this solution on YOUR website! 1) The songs can be played in any order:
No of ways the 9 songs can be played = 9! = 362880
Explanation: the 1st song can be chosen from any of the 9 songs, the 2nd played song can be chosen from the remanining 8 songs, the 3rd played song can be chosen from the remaining 6 songs, the 5th played song can be chosen from the remaining 5 songs, the 6th played song can be chosen from the remaining 4 songs, the 7th played song can be chosen from the remaining 3 songs, the 8th played song can be chosen from the remaining 2 songs and the 9th played song can be chosen from the remaining 1 song. Hence the no of ways = 9*8*7*....2*1 =9!
2) The first song must be a slow song and the last song must be a slow song.
No of ways the 1st song can be chosen = 5 (as there are 5 slow songs)
No of ways the 9th song can be chosen = 4 (as there are 4 remaining slow songs left)
Having chosen the 1st and 9th, the songs 2 thru 8 can be chosen in 7! ways
Total no of ways = 7!*5*4 = 100800 ways
3) The first two songs must be fast songs.
No of ways to select 1st song = 4 (as there are 4 fast songs)
No of ways to select 2nd song = 3 (as there are remaining 3 fast songs)
Having chosen 1st and 2nd song, the songs 3 thru 9 can be chosen in 7! ways
Total no of ways = 7!*4*3 = 60480
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