How many ways can someone pick 4 winners for 8 prizes if each prize is the same?

Question

Please tell me how you got the answer too

Answer 1

Well, if there are 8 people, then the answer is 8!/[4!(8-4)!]
= 8!/(4!4!)
= 8*7*6*5 / (4*3*2*1)
= 7*5*2 = 70

Answer 2

First make observations. (1) the prizes are the same; (2) the winners can not be indistinguishable; (3) each winner has to receive at least one prize. Hence, this is the problem to distribute 8 identical prizes among 4 winners such that each winner must receive at least one prize.
You can easily imagine that the 8 prizes are in a row and thus 7 spaces in between. Your task is to find the number of ways to put 3 sticks in the 7 spaces, such that the 8 prizes would be separated into 4 portions, and hence the first portion is for the first winner, and so on.
The solution is:
(7, 3) = 7*6*5/ (1*2*3) = 35
It is a neat idea to analyze the problem, is not it?