Himadri's Book Boxes

For each book, there are 3 boxes that it can go in.

Total # of ways = ways for 1st book * ways for 2nd book * ... * ways for 5th book = $3^{5}$ = 243.

The problem is equivalent to finding the number of functions $f: \{1,2,3,4,5\} \to \{1,2,3\}$ For each $a \in \{1,2,3,4,5\}$ , there are three possible values of $f(a)$ , hence the number is $$\boxed{3^5 = 243}$$

Each book has 3 options => 3^5 = 243 48char yolo

3^5 =243

The first book can be put in 3 boxes,i.e,3 ways.Similarly,all the other books can be put in 3 ways.Therefore total ways of putting books=3x3x3x3x3= 243

Every book can go to any box. So we have \­[(boxes)^{(books)} =3^{5}=243\­]

Since the order does not matter,hence there is 3 different ways to put one of the books into a box.

There are 5 distinct books, and hence, the number of ways = $3^5=243$

Para cada livro, Himadri tem 3 opções de caixas para onde colocá-los.

Assim, Ele tem 3 maneiras de acomodar o primeiro livro. Igualmente para o segundo, terceiro, quarto e quinto.

Portanto, o número de maneiras que Himadri pode colocar os livros é expresso por

$3\times3\times3\times3\times3=3^{5}=243$