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why is the following question a permutation and not a combination

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Joined: 29 May 2017
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why is the following question a permutation and not a combination  [#permalink]

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New post 13 Jul 2018, 05:28
In a group of 10 people, 3 prizes od $20, $10, and $5 are to be given. How many ways can the prizes be distributed?

answer is 720

the yt video says that orders matters in this....but how and why?
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why is the following question a permutation and not a combination  [#permalink]

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New post 13 Jul 2018, 07:59
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Lets think of the above question like this.

In a group of 10 people, 3 prizes of $20, $10, and $5 are to be given.

Lets assume there is another prize(Loser) that is given to all the other people who are not first, second or third.

Now the question becomes, in how many ways the four prizes can be given to 10 people

=> We need to pick 3 people for first three prizes and the remaining seven people we don't need to pick. Once we pick 1, 2 and 3 the remaining 7 will automatically gets the Loser prize.

Total number of ways to pick 10 people = \(10!\)

Since the above number also includes different ways of picking the remaining 7 people and we actually don't need to pick remaining 7, we divide 10! by 7!

=> \(\frac{10!}{7!}\) = 720

Hope this helps your understanding.
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Re: why is the following question a permutation and not a combination  [#permalink]

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New post 13 Jul 2018, 08:48
Also check this thread https://gmatclub.com/forum/permutations ... 10838.html

It has different types of permutation and combination problems to practice on.
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Re: why is the following question a permutation and not a combination &nbs [#permalink] 13 Jul 2018, 08:48
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