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# why is the following question a permutation and not a combination

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Manager
Joined: 29 May 2017
Posts: 107
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
why is the following question a permutation and not a combination  [#permalink]

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13 Jul 2018, 04:28
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? MBA Section Director Affiliations: GMATClub Joined: 22 May 2017 Posts: 1011 Concentration: Nonprofit GPA: 4 WE: Engineering (Computer Software) why is the following question a permutation and not a combination [#permalink] ### Show Tags 13 Jul 2018, 06:59 1 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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MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 1011
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
Re: why is the following question a permutation and not a combination  [#permalink]

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13 Jul 2018, 07:48
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, 07:48
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# why is the following question a permutation and not a combination

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