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# Seven people enter a race. There are 4 types of medals. Winner - plati

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Intern
Joined: 24 Nov 2015
Posts: 1
Seven people enter a race. There are 4 types of medals. Winner - plati  [#permalink]

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14 Dec 2015, 18:01
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:29) correct 32% (01:42) wrong based on 133 sessions

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Seven people enter a race. There are 4 types of medals. Winner - platinum, runner up - gold, next two racers - silver and the last 3 - bronze. Ways to do it?

a) 7!/3!
b) 7!/2!3!
c) 1*1*2!*3!
d) 7*6*2!*3!
e) 7*6*5*4

I want to understand why it cannot be 7x6x5x3?

The platinum medal can be won by 7 different people, the gold by 6,silver by 5 and bronze by 3. Where am I going wrong?

Math Expert
Joined: 02 Aug 2009
Posts: 7207
Re: Seven people enter a race. There are 4 types of medals. Winner - plati  [#permalink]

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14 Dec 2015, 22:05
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2
nithya16 wrote:
I read this problem on combinatorics today.
Seven people enter a race. There are 4 types of medals. Winner - platinum, runner up - gold, next two racers - silver and the last 3 - bronze.

I want to understand why it cannot be 7x6x5x3?

The platinum medal can be won by 7 different people, the gold by 6,silver by 5 and bronze by 3. Where am I going wrong?

Hi,
the reason why you are going wrong in your approach is that you are not selecting the number for silver and bronze correctly..
let me take the approach adopted by you..
platinum-7 different people..
gold- remaining 6 different people..
silver- 2 out of remaining 5=5C2= 5!/2!3!...
bronze - 1 as all the three remaining are getting it..

total ways= 7*6*5!/2!3!=7!/2!3!..
hope it helped
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: Seven people enter a race. There are 4 types of medals. Winner - plati  [#permalink]

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18 Apr 2018, 21:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Seven people enter a race. There are 4 types of medals. Winner - plati &nbs [#permalink] 18 Apr 2018, 21:24
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