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combination/permutation w/ restricted items

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pws
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combination/permutation w/ restricted items [#permalink] New post   10 Aug 2006, 15:30
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.



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Re: combination/permutation w/ restricted items [#permalink] New post   10 Aug 2006, 15:39
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
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Re: combination/permutation w/ restricted items [#permalink] New post   10 Aug 2006, 16:56
2*8*7*6*5*4*3*2*1*1 = 80640
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Re: combination/permutation w/ restricted items [#permalink] New post   10 Aug 2006, 17:21
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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Re: combination/permutation w/ restricted items [#permalink] New post   11 Aug 2006, 00:22
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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Re: combination/permutation w/ restricted items [#permalink] New post   11 Aug 2006, 01:04
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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Re: combination/permutation w/ restricted items [#permalink]
11 Aug 2006, 01:04
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