Question 907713: HELP PLEASE!!!!
Q. Number of different ways in which 8 different books can be distributed among 3 students, if each student receives at least 2 books.
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website! Q. Number of different ways in which 8 different books can be
distributed among 3 students, if each student receives at least 2 books.
They can be distributed 2,2, and 4 or 2,3, and 3
Case 1. 2,2, and 4
We choose the student to get 4 books in 3 ways.
We choose the 4 books to give to that student in 8C4 ways
We then choose one of the other students, it doesn't matter which one.
We give that student 2 of the remaining 4 books in 4C2 ways.
The other student automatically gets the remaining 2 books in 1 way.
That's 3*8C4*4C2*1 = 3*70*6*1 = 1260 ways
Case 2. 2,3, and 3
We choose the student to get 2 books in 3 ways.
We choose the 2 books to give to that student in 8C2 ways
We then choose one of the other students, it doesn't matter which one.
We give that student 3 of the remaining 6 books in 6C3 ways.
The other student automatically gets the remaining 3 books in 1 way.
That's 3*8C2*6C3*1 = 3*28*20*1 = 1680 ways
Total = 1260+1680 = 2940
Edwin
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