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Permutation vs Combination

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Permutation vs Combination

by vineetbatra » Sat Jun 13, 2009 8:33 am
Mike, a DJ at a high school radio station, neeeds to play two or three more songs before the end of the school dance. if each composition must be selected from a list of 10 most popular songs of the year, how many song sequences are available for the remainder of the dance.

1. 6
2. 90
3. 165
4. 720
5. 810

Is this a combination problem or a permutation problem, and why?
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Re: Permutation vs Combination

by dtweah » Sat Jun 13, 2009 10:46 am
vineetbatra wrote:Mike, a DJ at a high school radio station, neeeds to play two or three more songs before the end of the school dance. if each composition must be selected from a list of 10 most popular songs of the year, how many song sequences are available for the remainder of the dance.

1. 6
2. 90
3. 165
4. 720
5. 810

Is this a combination problem or a permutation problem, and why?
From the phrasing it would appear that any song played would give equal satistaction so it does not matter the order in which songs are chosen. All the songs are grouped under "10 most popular" heading so order of ranking is not important. That ought to make it a combination problem.
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Re: Permutation vs Combination

by Ian Stewart » Sat Jun 13, 2009 11:03 am
vineetbatra wrote:Mike, a DJ at a high school radio station, neeeds to play two or three more songs before the end of the school dance. if each composition must be selected from a list of 10 most popular songs of the year, how many song sequences are available for the remainder of the dance.

1. 6
2. 90
3. 165
4. 720
5. 810

Is this a combination problem or a permutation problem, and why?
If the question asks how many 'sequences' are possible, then order is certainly important; it's a permutations question, not a combinations question. That said, the wording of the question is pretty bad. Parts of it aren't even grammatical, and it isn't at all clear whether Mike is allowed to play the same song twice. From the answer choices, it's clear he's not; if he plays two songs, he has 10 choices for the first and 9 for the second, so 10*9 = 90 sequences in total. If he plays three songs he has 10, 9 and 8 choices, so 10*9*8 = 720 sequences in total, giving us a total of 90 + 720 = 810 sequences.
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by vineetbatra » Sun Jun 14, 2009 2:29 pm
Thanks Ian, i.e. the correct answer.
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