Question

There are 5 almirahs in village library. Each almirah has 264 books. How many books are there in 5 almirahs. ​

Answer 1

Answer:

Here we assume that the books and shelves are distinguishable. First of all, there are 3 ways to divide the books among the shelves: 1) all 3 on one shelf; 2) 2 on one shelf and 1 on another; 3) each book on a separate shelf. And for any given arrangement among the shelves, there are 3!=6 ways of distributing the books in the given “slots". Since there are 5 shelves, the first case has 5 ways of placing the books. In the second case, since there are 3 empty shelves, there are 5!3! =20 ways of arranging the books. In the third case, since there are 3 non-empty and 2 empty shelves, there are 5!3!2! =10 ways of arranging the books. Summing this up we have 6(5+20+10)=6⋅35=210 ways of arranging 3 books on 5 shelves.

Addendum:

Another way of doing problems like this is to consider the shelves (except for the bottom one) as indistinguishable books and find the permutations of the whole lot. This leads to the general formula, (b+s−1)!(s−1)! . In this case we get 7!4!=210 .

Answer 2

Answer:

264×5

1320 books in 5 almirah

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