1. ## contest

There is a contest. 5 students will attend to this contest. 6 different books will be given as the prize. Winner will get 3 books, seond 2 books, and third student will get 1 book. In how many ways we can distribute the prizes?

My work:
C(6,3).C(3,2).C(2,1)

But the answer is 3600 according to the book.

2. ## Re: contest

5 ways of picking 1st place winner
4 ways of picking 2nd place winner
3 ways of picking 3rd place winner
$\dbinom{6}{3}$ ways of choosing 3 books for 1st place
$\dbinom{3}{2}$ ways to choose 2 books for 2nd place
$\dbinom{1}{1}$ way to choose 1 book for 3rd place
Product principle says since each step is independent from the previous steps, take the product.

3. ## Re: contest

I also found 60. Book's answer is wrong.

4. ## Re: contest

Originally Posted by kastamonu
I also found 60. Book's answer is wrong.
No, the book is correct. By the product principle, the number of ways to distribute the prizes is:
$5\cdot 4\cdot 3\cdot \dbinom{6}{3}\cdot \dbinom{3}{2}\cdot \dbinom{1}{1} = 3600$

5. ## Re: contest

Correct I only distributed the books. Many Thanks.

6. ## Re: contest

Originally Posted by kastamonu
There is a contest. 5 students will attend to this contest. 6 different books will be given as the prize. Winner will get 3 books, seond 2 books, and third student will get 1 book. In how many ways we can distribute the prizes?
My work:
C(6,3).C(3,2).C(2,1) But the answer is 3600 according to the book.
Take six blank cards. Mark a one on three of them; mark a two on two of them; mark a one on one card.
How many ways can those marked cards is a row?
$\dfrac{6!}{3!\cdot 2!\cdot 1!}=60$ SEE HERE