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

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
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.
(edited 6 years ago)
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
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
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.
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
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
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!
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.
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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