Question

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

• A. $n^p$
• B. $p^n$
• C. ${(p+1)}^n-1$
• D. ${(n+1)}^p-1$

Answer 1

Answer: (C)

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

In case of each book we may take $0,1,2,3,\dots ,p$ copies, i.e., we may deal with each book in $(p+1)$ ways and therefore with all the books in ${(p+1)}^n$ ways.

But this includes the case where all the books rejected and no selection is made.

So, the number of ways in which selection can be made $={(p+1)}^n-1$.