Probability and Statistics - Permutations question Watch

mygjjgknj
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A library contains 4 identical copies of book A, 2 identical copies of book B and 5 identical copies of
book C. These 11 books are arranged on a shelf in the library.

ii) Calculate the number of different arrangements if all the books A are next to each other and none
of the books B are next to each other.


The question is from CIE 9709 May-June 2017 paper 62. Any help will be appreciated.
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BobbJo
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consider [AAAA] as a single object
you have to arrange [AAAA] B B C C C C C
so that B are not together

one method is
arrange [AAAA] and the 5 C's first
e.g * [AAAA] * C * C * C * C * C *
this creates 7 places (marked *) for the B's.
hence number of arrangements is found

another method is
find number of arrangements when B's are together, i.e of [AAAA] [BB] C C C C C
subtract from no restrictions on B's & A's together
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mygjjgknj
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I have one question. I saw in the examiner report that an error is to arrange AAAA and multiply with 4! . How come AAAA doesn't have to be arranged? Is it because they are identical?
(Original post by BobbJo)
consider [AAAA] as a single object
you have to arrange [AAAA] B B C C C C C
so that B are not together

one method is
arrange [AAAA] and the 5 C's first
e.g * [AAAA] * C * C * C * C * C *
this creates 7 places (marked *) for the B's.
hence number of arrangements is found

another method is
find number of arrangements when B's are together, i.e of [AAAA] [BB] C C C C C
subtract from no restrictions on B's & A's together
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ghostwalker
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(Original post by mygjjgknj)
I have one question. I saw in the examiner report that an error is to arrange AAAA and multiply with 4! . How come AAAA doesn't have to be arranged? Is it because they are identical?
If the 4! is refering to the A's, then yes: Since you cannot distinguish between the individual A's there is only one possible arrangement of them.
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mygjjgknj
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I see, thank you!
(Original post by ghostwalker)
If the 4! is refering to the A's, then yes: Since you cannot distinguish between the individual A's there is only one possible arrangement of them.
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