Question 1037064: At a baby shower, 15 guests are in attendance and 3 of them are randomly selected to receive a door prize.
Question: If all 5 prizes are different, in how many ways can the prizes be awarded?
I came up with 5x5x5=125 or 5^3 am I doing this right?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! probably not.
5 prizes being given to 3 people.
presumably each person will be given only 1 prize.
in that case, then 5C3 sound like the correct formula.
5C3 = 5! / (3! * 2!) = (5*4*3!) / (3!*2!) = (5*4)/2!= (5*4)/2 = 10.
there are 10 ways that 3 people can each receive 1 out of 5 possible prizes.
let's assume the prizes are a,b,c,d,e.
that's 5 in total.
1 prize will be given to each of 3 people.
the possible ways that each of 3 people can receive the prizes would be:
a,b,c
a,b,d
a,b,e
a,c,d
a,c,e
a,d,e
b,c,d
b,c,e
b,d,e
c,d,e
a,b,c means that person 1 gets a, person 2 gets b, person 3 gets c.
a,b,d means that person 1 gets a, person 2 gets b, person 3 gets d.
etc.....
5*5*5 doesn't work because then you have the possibility that more than 1 person can get the same prize at the same time, which is impossible.
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