Question 1037064
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.