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# combination/permutation w/ restricted items

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Intern
Joined: 16 Jul 2006
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combination/permutation w/ restricted items [#permalink]  10 Aug 2006, 14:30
I can't seem to answer this one:

Tom is making a CD containing 10 of his favorite songs. He has chosen 2 bues songs and 8 rock songs to be on the cd. The blues songs will be the first and the last songs. How many different orderings of songs on the CD are possible?

thanks.
SVP
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I am still struggling my way through this P&C problems.

But i will post my replu either ways it is good to argue about approaches any ways.

8 of the songs in the middle have 8! ways of arranging

The other two songs have two different displays(first ,last) or l(ast and first)

Thus total possibilities are 8!*2

Hope this is right
Senior Manager
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2*8*7*6*5*4*3*2*1*1 = 80640
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2*8!

2 because 1st and last can be arranged in 2 ways. There are other 8 slots and that forms a permutation of 8! => total is 2*8!
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SVP
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Clear 2*8!

Blues can be arranged in 2! ways = 2
Rock can be arranged in 8! ways

hence total = 2*8!
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Label the blues songs as BA and BB. We're told the blues song make the first and last songs.

So the ordering can be BA _ _ _ _ _ _ _ _ _ BB or BB _ _ _ _ _ _ _ _ _ BA

For the first one, there are 8! ways to order the songs. The second one is the same.

Total = 2(8!)
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