Math Is Fun Forum

fibi200329

Guest

Permutation Questionnn~ plz help

a group of 8 students want to be seated in 8 seats. find all possible number of arrangments for the following cases

1)none of and 2 boys or 2 girls is side by side
2)boys can not be side by side
3)there must be exactly 3 students between student A and B

please also include an explaination for each subquestion, im really stuck
thank you

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Permutation Questionnn~ plz help

Hi fibi200329;

Shouldn't you mention how many boys and girls there are?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Permutation Questionnn~ plz help

A group of 8 students want to be seated in 8 seats.
Find all possible number of arrangments for the following cases:

1) No two boys or two girls are side by side

2) Boys can not be side by side

3) There must be exactly 3 students between student A and B

.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Permutation Questionnn~ plz help

Hi soroban;

Since A can be any student and B can be any student shouldn't there be 56 permutations of A and B:

56 * 2 * 4 * 6! = 322560 ways

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Permutation Questionnn~ plz help

I think soroban has it right. If you generalise who A and B are, the question is essentially saying "there must be some students who have three students between them", in which case, every combination works.

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Why did the vector cross the road?
It wanted to be normal.