SOLUTION: In how many ways can 12 books be divided between A and B so that one may get 9 books and the other student 3 books? Here is how I did it: 12C3 + 3C3 = 220+1 = 221 ways OR

Algebra ->  Algebra  -> Permutations -> SOLUTION: In how many ways can 12 books be divided between A and B so that one may get 9 books and the other student 3 books? Here is how I did it: 12C3 + 3C3 = 220+1 = 221 ways OR       Log On

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Question 475749: In how many ways can 12 books be divided between A and B so that one may get 9 books and the other student 3 books?
Here is how I did it:
12C3 + 3C3 = 220+1 = 221 ways
OR
12C3 +9C9 = 220 + 1 = 221 ways.
The book's answer is 2*12C9 = 2*12C3 = 440 ways. But why my answer is not correct? Isn' t it true that once student A takes 9 books there are only three books left for the second student. So, that's why my calculation makes sense.
Could you help me explain why the textbook is right? Thank you very much.
I.
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!
12 books be divided between A and B so that one may get 9 books and the other student 3 books.
case 1: when A will get 9 books and B will get 3 books
number of ways = 12C9 * 3C3 = 220

case 2: when A will get 3 books and B will get 9 books
number of ways = 12C3 * 9C9 = 220

total number of ways = 220 + 220 = 440

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