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Statistics as level cie math , help please (1 question) watch

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    2 spaniels, 2 retrievers and 3 poodles go through to the final. They are placed in a line.

    (ii) How many different arrangements of these 7 dogs are there if the spaniels stand together and the retrievers stand together? [3]
    The answer is 2!x2!x5!

    Why is the answer like that ? Where did the five come from ? Please explain , thank u
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    (Original post by Sammysammy99)
    2 spaniels, 2 retrievers and 3 poodles go through to the final. They are placed in a line.

    (ii) How many different arrangements of these 7 dogs are there if the spaniels stand together and the retrievers stand together? [3]
    The answer is 2!x2!x5!

    Why is the answer like that ? Where did the five come from ? Please explain , thank u
    If the spaniels stand together as a pair, we can initially trreat them as one item, similarly the retrievers. Hence there are 1+1+3= 5 items.

    But there are actually 2 spaniels, and can be in any order S1 S2, or S2 S1. There are 2! such orderings hence we multply by 2! for the spaniels and simiarly for the retrievers.
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    (Original post by ghostwalker)
    If the spaniels stand together as a pair, we can initially trreat them as one item, similarly the retrievers. Hence there are 1+1+3= 5 items.

    But there are actually 2 spaniels, and can be in any order S1 S2, or S2 S1. There are 2! such orderings hence we multply by 2 for the spaniels and simiarly for the retrievers.
    But it says different arrangement of the seven dogs , how is that answer correct , why are we multiplying by 5! , there are 3 poodles
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    (Original post by ghostwalker)
    If the spaniels stand together as a pair, we can initially trreat them as one item, similarly the retrievers. Hence there are 1+1+3= 5 items.

    But there are actually 2 spaniels, and can be in any order S1 S2, or S2 S1. There are 2! such orderings hence we multply by 2! for the spaniels and simiarly for the retrievers.
    I do not get it , what happened to the poodles
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    (Original post by Sammysammy99)
    But it says different arrangement of the seven dogs , how is that answer correct , why are we multiplying by 5! , there are 3 poodles
    There are 5 items to arrange:

    A pair of spaniels - together. One item

    A pair of retrievers - together. One item.

    Three poodles.

    Total of 5 items.

    The pair of spaniels is actually 2 dogs together and they can be in a total of 2! possible arrangements - together. So, we multiply by 2!.

    Similarly the retrievers.
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    (Original post by ghostwalker)
    There are 5 items to arrange:

    A pair of spaniels - together. One item

    A pair of retrievers - together. One item.

    Three poodles.

    Total of 5 items.

    The pair of spaniels is actually 2 dogs together and they can be in a total of 2! possible arrangements - together. So, we multiply by 2!.

    Similarly the retrievers.
    Then where do the poodles fall in this situation , did you take into account that there are 3 poodles
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    (Original post by ghostwalker)
    There are 5 items to arrange:

    A pair of spaniels - together. One item

    A pair of retrievers - together. One item.

    Three poodles.

    Total of 5 items.

    The pair of spaniels is actually 2 dogs together and they can be in a total of 2! possible arrangements - together. So, we multiply by 2!.

    Similarly the retrievers.
    Can u please do it , and multiply them , my question is to be exact why do we write 5! Instead of 3! , the other two places are taken
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    (Original post by Sammysammy99)
    Can u please do it , and multiply them , my question is to be exact why do we write 5! Instead of 3! , the other two places are taken
    Why do we write 5! Instead of 3!
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    (Original post by Sammysammy99)
    Then where do the poodles fall in this situation , did you take into account that there are 3 poodles
    They count as 3 in the 5 items.

    If we label them p1,p2,p3, then one possibe initial arrangement is:

    p1 (2 retrievers) p3 p2 (2 spaniels)

    There are 5! such arrangements.
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    (Original post by ghostwalker)
    They count as 3 in the 5 items.

    If we label them p1,p2,p3, then one possibe initial arrangement is:

    p1 (2 retrievers) p3 p2 (2 spaniels)

    There are 5! such arrangements.
    Alright thank you
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