Question

In how many ways you can put 20 books on 50 shelves so that there is not more than one book on a shelf?

Answer 1

Answer:

The other answer I saw is the same way that I used to explain in my class as well. But, there's an alternative way to reach the answer as well

First thing that we should know is that if there are 'n' units kept in a row, then there are 'n+1' gaps generated by them. So, what we should understand is that when there is no item there is 1 gap, when there is one item there are 2 gaps, and so on.

Let us use that concept here, with a small variation: the 5 shelves are 5 initial gaps. The first book has 5 choices (5 initial gaps) to go to. Once we have placed this book, there are now 6 gaps on which the 2nd book can be placed. After the 2nd book is placed, there are 7 gaps in which 3rd book can be placed, and so on.

So, the total arrangements will be = 5*6*7*...24 [as there are 20 books] = 24P20