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.

Official answer : 7!/(2!*3!)

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?

Can someone please help?

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

_________________

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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