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Carrotsticks

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Sorry - I'm confused as to why it's this.
XXXXX(AB)XXX

So we have 9 elements there (we count the AB as a group since they are together), but they are in a circle, so 8!.

Now A and B can swap, so 2!.

Therefore 8!2!.
 

theind1996

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XXXXX(AB)XXX

So we have 9 elements there (we count the AB as a group since they are together), but they are in a circle, so 8!.

Now A and B can swap, so 2!.

Therefore 8!2!.
Oh - thanks a lot :)

Don't know why, but I always get confused with circles.

Thanks heaps :)
 

RivalryofTroll

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Question: How do we know when to use the multiplication principle? Is there a certain way that the question is asked to hint us to use it?
 

Carrotsticks

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Question: How do we know when to use the multiplication principle? Is there a certain way that the question is asked to hint us to use it?
If you're working on a single case and doing everything at once, then multiply.
 

RivalryofTroll

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A meeting room contains a round table surrounded by ten chairs.
These chairs are indistinguishable and equally spaced around the table.

(a) A committe of 10 people incl. 3 teens. How many arrangements are there in which all 3 sit together? 30240

(b) Elections are held for the positions of Chairperson and Secretary in a 2nd committee of ten people seating around this table. How many seating arrangements are there in which two people elected are sitting directly opp. to each other?
 

Deliriously

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A committee of 6 is to be selected from 10 people of whom A and B are two. How many committees can be formed excluding A if B is included?
10 people to choose to form 6.

For this question, there are two cases:
When B is included (A must be excluded) - 8 (b/c B has to be included and A excluded) to choose from 5 ( B is already in) .'. 8C5
When B is excluded (A doesn't have to be excluded)- 9 (B is excluded) to choose from 6 (anyone else can be chosen) .'. 9C6
= 8C5+9C6 = 140
 

theind1996

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10 people to choose from 6.

For this question, there are two cases:
When B is included (A must be excluded) - 8 (b/c B has to be included and A excluded) to choose from 5 ( B is already in) .'. 8C5
When B is excluded (A doesn't have to be excluded)- 9 (B is excluded) to choose from 6 (anyone else can be chosen) .'. 9C6
= 8C5+9C6 = 140
Doesn't the question ask to include B?
 

RivalryofTroll

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10 people to choose to form 6.

For this question, there are two cases:
When B is included (A must be excluded) - 8 (b/c B has to be included and A excluded) to choose from 5 ( B is already in) .'. 8C5
When B is excluded (A doesn't have to be excluded)- 9 (B is excluded) to choose from 6 (anyone else can be chosen) .'. 9C6
= 8C5+9C6 = 140
Thanks very much.

For my most recent question above, is it just 8! = Answer ?
 

Carrotsticks

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I think it depends on how you read the question, and placement of commas.

How I interpreted it:

A committee of 6 is to be selected from 10 people of whom A and B are two. How many committees can be formed excluding A, if B is included?

What the question presumably tried to communicate

A committee of 6 is to be selected from 10 people of whom A and B are two. How many committees can be formed, excluding A if B is included?
 

theind1996

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I think it depends on how you read the question, and placement of commas.

How I interpreted it:

A committee of 6 is to be selected from 10 people of whom A and B are two. How many committees can be formed excluding A, if B is included?

What the question presumably tried to communicate

A committee of 6 is to be selected from 10 people of whom A and B are two. How many committees can be formed, excluding A if B is included?
English... haunts you to this day.
 

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