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The choir consists of 5 boys and 6 girls. In how many ways

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Director
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The choir consists of 5 boys and 6 girls. In how many ways [#permalink] New post 10 Oct 2007, 22:36
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The choir consists of 5 boys and 6 girls. In how many ways can the singers be arranged in a row, so that all the boys are together? (assume all members of the group are uniform and combinations within the group do not matter).

A 120
B 30
C 24
D 11
E 7
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Re: PS_probability_chord [#permalink] New post 10 Oct 2007, 23:20
IrinaOK wrote:
The choir consists of 5 boys and 6 girls. In how many ways can the singers be arranged in a row, so that all the boys are together? (assume all members of the group are uniform and combinations within the group do not matter).

A 120
B 30
C 24
D 11
E 7




E. 7 Since members are uniform.

Let [B] be a cluster of boys such that all 5 are next to eachother.

_G_G_G_G_G_G_

We see that there is exactly 7 places for [B] to go (marked as an underscore [_])
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 [#permalink] New post 11 Oct 2007, 03:16
I have seen this question before, but it could be 7 true, but it could be higher if only the group of boys is to be counted as a group. If the girls can be rearranged then...it will be higher
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 [#permalink] New post 11 Oct 2007, 07:29
Not very well worded, but 7 seems right:

0B6
1B5
2B4
3B3
4B2
5B1
6B0
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Re: PS_probability_chord [#permalink] New post 09 Jan 2008, 09:19
11 - 6 +1 = 7 elements to arrange

since the elements are uniform, we need to account for 6! repeats.

7!/6! = 7
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Re: PS_probability_chord [#permalink] New post 09 Jan 2008, 17:35
Got 7 as well. I thought about it like this:

_ _ _ _ _ _ _ _ _ _ _

There's 11 spots to fill, and the five boys have to be together. Start from the left and take up the first 5 spots: thats one way. Then, move one spot to the right, and take up the next 5, thats two ways. Keep going until you run out of space and youll see there are only 5 ways.

One thing to note is that the stem said that a different arrangements dont matter. If it did, we'd have many more ways, since in each 'way', the boys can be arranged in 5! ways.
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Re: PS_probability_chord [#permalink] New post 09 Jan 2008, 18:57
IrinaOK wrote:
The choir consists of 5 boys and 6 girls. In how many ways can the singers be arranged in a row, so that all the boys are together? (assume all members of the group are uniform and combinations within the group do not matter).

A 120
B 30
C 24
D 11
E 7


I couldnt figure out how to do this via combinatorics equations so I just wrote it down.

BBBBBGGGGGG. Had bout 30sec left and it dawned on me that all we have to realize is that we can arrange it

GBBBBBGGGGG, GGBBBBBGGGG etc... I count 7. U dont have to write all of these out just realize u can have 5 inbetween G's and 2 on the outside.
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Re: PS_probability_chord [#permalink] New post 28 Sep 2009, 10:28
The choir consists of 5 boys and 6 girls. In how many ways can the singers be arranged in a row, so that all the boys are together? (assume all members of the group are uniform and combinations within the group do not matter).

A 120
B 30
C 24
D 11
E 7


Soln. Since combinations within the group not matter, and since all boys go together. We can group all 5 boys into 1 group. The 6 girls and the 1 group of boys can be arranged in 7 ways.

Ans is E
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Re: PS_probability_chord [#permalink] New post 02 May 2011, 22:25
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total = 6 girls + 1 (set of boys together)
permutation = 7!/ 6!(set of girls can be arranged in 6! ways)
7
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Re: PS_probability_chord   [#permalink] 02 May 2011, 22:25
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The choir consists of 5 boys and 6 girls. In how many ways

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