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Need Help With Permutation

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Hey guys, it's been a while since I posted a question.

I have a problem. I can't really seem to figure out if a situation requires a permutation or combination type of solving.

A football competition is organised between 8 teams. In how many ways can the top 4 places be filled in order of premiership points obtained?

The answer is 1680. To get this answer you need to do: 8*7*6*5

This is for permutation. For combination, you'll have to divide this by 4*3*2*1.

What do I have to do, and why?

Thanks

Aug 3, 2018

#1
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Isn't it a simple case of permutations and combinations???

Permutations =8 nPr 4 =8! / (8 - 4)! =40,320 / 24 =1,680

Combinations =8 nCr 4 = 8! / [(8 - 4)! * 4!]=40,320 / (24 x 24) =70

Aug 3, 2018
#2
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Yeah. But I wanted to know how to find out if this situation was a permutation or combination (without knowing the answer)

When there are 4 out of 8 teams that are going to fill out the top 4, is it a permutation or combination? And why?

Does top 4 mean there is an order? Because that would mean it would be a permutation.

Or does top 4 means any random team can enter? Because that would mean it would be a combination (I think...)

Thanks though!

Gh0sty15  Aug 3, 2018
#3
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Permutation: A set of objects in which position (or order) is
important. Example: a,b, c, d

{a, b, c, d} | {a, b, d, c} | {a, c, b, d} | {a, c, d, b} | {a, d, b, c} | {a, d, c, b} | {b, a, c, d} | {b, a, d, c} | {b, c, a, d} | {b, c, d, a} | {b, d, a, c} | {b, d, c, a} | {c, a, b, d} | {c, a, d, b} | {c, b, a, d} | {c, b, d, a} | {c, d, a, b} | {c, d, b, a} | {d, a, b, c} | {d, a, c, b} | {d, b, a, c} | {d, b, c, a} | {d, c, a, b} | {d, c, b, a} (total: 24)

Combination: A set of objects in which position (or order) is NOT
important. Example:a,b, c,d =1 combination only. The order of the letters DOES NOT MATTER.

Aug 3, 2018
#4
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Oh. But isn't "abcd" one combination as well in a permutation? There isn't another "abcd"

Gh0sty15  Aug 3, 2018
#5
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Both of them start with: a,b,c, d. But, in permutation, you can move the LETTERS around. So, a,b, c, d is NOT the same as: a, c, b, d. They are 2 different permutations.

But in combinations, a,b, c, d AND a, c, b, d ARE THE SAME.

Look at it this way. If there are 4 people, Alice, Bob, Carol, and Dave.

In combinations, no matter how they stand together for a picture, they are considered ONE combination.

But for permutations, you can move them around for a picture. And EACH move is considered a different permutation such as: Alice, Dave, Carol, Bob.

So, you can move them around 4! =24 times for 24 different pictures, or 24 different permutations.

Aug 3, 2018