There are $n$ different books and $p$ copies of each. The number of ways in which a selection can be made from them, is

In the case of each book we may take 0, l, 2, 3,….$p$

copies; that is, we may deal with each book in $p + 1$ wavs and 

therefore with all the books in ${(p + 1 )}^n$ ways But, this includes 

the case where all the books are rejected and no selection is made.

$\therefore$ Number of ways in which selection can be made

$={(p+1)}^n-1.$