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    Hello everyone! I need some help on this question from a October/November 2011 S1 paper.


    Find the number of different ways in which the 9 letters of the word GREENGAGE can be arranged if exactly two of the Gs are next to each other.

    The marking scheme says that one of the solutions is such that
    8!/3! – 2 × 7!/3!

    I managed to obtain 8!/3! - 7!/3! instead. Why must we multiply 7!/3! by 2? I hope someone can explain this, it'll really be a great help
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    (Original post by Southpaw Wolf)
    Hello everyone! I need some help on this question from a October/November 2011 S1 paper.


    Find the number of different ways in which the 9 letters of the word GREENGAGE can be arranged if exactly two of the Gs are next to each other.

    The marking scheme says that one of the solutions is such that
    8!/3! – 2 × 7!/3!

    I managed to obtain 8!/3! - 7!/3! instead. Why must we multiply 7!/3! by 2? I hope someone can explain this, it'll really be a great help
    I'm not a huge fan of perms and combs, but since no-one's replied I figured I'd give it a go.
    I think the reason is that the G's grouped together need to be multiplied by 2! as there are two possible arrangements within the grouped G's.
    So when you subtract the ways in which 3 G's are together you need to account for the two possible arrangements.

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    My preferred method for this would be to group to G's, fix the third in place then:
    \dfrac{2! \times ^3\mathrm{C}_2 \times 7!}{3!}
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    (Original post by joostan)
    I'm not a huge fan of perms and combs, but since no-one's replied I figured I'd give it a go.
    I think the reason is that the G's grouped together need to be multiplied by 2! as there are two possible arrangements within the grouped G's.
    So when you subtract the ways in which 3 G's are together you need to account for the two possible arrangements.

    Spoiler:
    Show
    My preferred method for this would be to group to G's, fix the third in place then:
    \dfrac{2! \times ^3\mathrm{C}_2 \times 7!}{3!}
    I assume the two possible arrangements would be GG and G1? Sorry if I don't make much sense, I meant if it was the two grouped G's and the single G.
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    (Original post by Southpaw Wolf)
    I assume the two possible arrangements would be GG and G1? Sorry if I don't make much sense, I meant if it was the two grouped G's and the single G.
    I'm sorry I don't understand your query
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    (Original post by joostan)
    I'm sorry I don't understand your query
    It's alright, I think I got it already. Thanks!
 
 
 
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