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by mehrasa » Mon Sep 19, 2011 8:48 am
There are four contestants in the competition for 6 different prizes. Each contestant can win one prize. How many different outcomes are possible at the competition for the four contestants?

A) 15

B) 30

C) 60

D) 180

E) 360
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by cans » Mon Sep 19, 2011 9:01 am
6 prizes. select 4: 6C4 =15
Give them..4!
thus 15*24=360
IMO E
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by mehrasa » Mon Sep 19, 2011 9:14 am
i thought that there are 4 contestant and 6 prizes so 24 ways they can be distributed among contestants.. how i could understand this is such Q.. i,m truly confused
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by shankar.ashwin » Mon Sep 19, 2011 9:18 am
You are right, but that is only the first part of the problem. Now after selecting the 4 gifts from the 6 (6c4), we can distribute the 4 gifts to 4 people in 4! ways, so multiply by 4!. (So that it includes each one getting a different gift)

So 6c4*4!

mehrasa wrote:i thought that there are 4 contestant and 6 prizes so 24 ways they can be distributed among contestants.. how i could understand this is such Q.. i,m truly confused
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by cans » Mon Sep 19, 2011 9:23 am
mehrasa wrote:i thought that there are 4 contestant and 6 prizes so 24 ways they can be distributed among contestants.. how i could understand this is such Q.. i,m truly confused
4! is correct. but you have to give 4 prizes... and you have 6. so you have to select those 2 prizes also...
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by tailoc » Mon Sep 19, 2011 10:39 am
6 prizes is different.

First one can win any a prize of 6 prizes ---> 6 ways
Second one can win any a prize of 5 prizes remaining ---> 5 ways
Likewise, third one --->4 ways, and fourth one ---> 3 ways
So, 6*5*4*3 = 360 ways
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