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
combination
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- cans
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6 prizes. select 4: 6C4 =15
Give them..4!
thus 15*24=360
IMO E
Give them..4!
thus 15*24=360
IMO E
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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!
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
- cans
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4! is correct. but you have to give 4 prizes... and you have 6. so you have to select those 2 prizes also...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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Cans!!
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
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