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

1. 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]

Why is the answer like that ? Where did the five come from ? Please explain , thank u
2. (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]

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.
3. (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
4. (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
5. (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.
6. (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
7. (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
8. (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!
9. (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.
10. (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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