SOLUTION: In how many ways can 8 different prizes be distributed equally among 4 students ?

Algebra ->  Probability-and-statistics -> SOLUTION: In how many ways can 8 different prizes be distributed equally among 4 students ?      Log On


   

Question 1161023: In how many ways can 8 different prizes be distributed equally among 4 students ?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

You can award the first student giving him (or her) any two of these 8 prizes;
             you can do it by %288%2A7%29%2F2 = 28 different ways.


Next,        you can award the 2-nd student giving him (or her) any two of remaining 6 prizes;
             you can do it by %286%2A5%29%2F2 = 15 different ways.


Next,        you can award the 3-rd student giving him (or her) any two of remaining 4 prizes;
             you can do it by %284%2A3%29%2F2 = 6 different ways.


Finally,     you can ONLY award the 4-th student giving him (or her) the remaining 2 prizes;
             you can do it by only one way - you just have no any other choice.


So, the ANSWER to the problem's question is THIS PRODUCT 28*15*6 = 2520 ways.

Solved.