Maths(permutation)
posted by Nada on .
A teacher prepares 5 different books for 7 students.If each student can get one or no book from the teacher , find the number of ways of distributing the books among the students.
can u explain it to me detailly.i have thought about this question for serveral hours but i still cant get the answer

This is a tricky question.
The teacher prepares 5 books for 7 students, but did not say that all five books HAVE to be distributed. So my interpretation is that 0 to 5 books could have been distributed.
For the case of 0 book distributed, there is only one way: no one gets any book.
For 1 book distrbuted, there are 7 ways to distribute, one for each student.
For 2 books distributed, there are 7 ways for the first book, 6 ways for the second. The order of the books is not important because they are different. There are 7!/(72)! ways.
Continue until all 5 books are distributed for a total of
1+7+42+210+840+2520=3620 ways 
but the correct ans is 2520,why?

As I indicated, this is a trick question.
I have assumed that not all five books need to be distributed because the question says the teacher "prepares" 5 books, and any student can take "one or no book". It did not say he "distributes" 5 books.
The answer assumes ALL five books are distributed, as you can verify with the last entry on my list, or 7!/2!