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permutation

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kksekar Just gettin' started! Default Avatar
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permutation Post Mon May 07, 2012 9:32 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    of the 6 letters of the word square.
    a) In how many of them is r the second letter? _ r _ _ _ _
    b) In how many of them are q and e next to each other?

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    Post Mon May 07, 2012 9:43 am
    a) If we set r in the second spot, there are 5 spots for 5 letters. 5!=120

    b) We can put qe next to each other in the following ways:

    q e _ _ _ _
    _ q e _ _ _
    _ _ q e _ _
    _ _ _ q e _
    _ _ _ _ q e

    For each of these, we have 4 spots for 4 letters: 4!=24. 24*5=120. However, for each of the arrangements we identified, we can reverse the order of q and e, so we need to double that total. 120*2=240.

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    aneesh.kg GMAT Destroyer!
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    Post Mon May 07, 2012 11:02 am
    We have these alphabets to use:
    S,Q,U,A,R,E.

    a) R has the be the second letter. The remaining 5 alphabets can be arranged on the remaining places in 5! = 120 ways.

    b) Since Q and E have to together, lets first group them like this: (Q, E) and treat it as one single entity.
    We have these 5 entities now to be arranged: (Q,E),S,U,A,R
    They can be arranged in 5! ways. But, the Q and E can be arranged inside the bracket in 2! ways because the question has not mentioned that Q has to come before E.
    Total number of ways = 5!*2! = 120*2 = 240

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