Question

There are $n$ books having $p$ 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)

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

For each book, we have $p$ copies. Thus each book can be dealt in $(p+1)$ ways.

Thus n books can be dealt in ${(p+1)}^n$ ways

This includes the cases when all books are rejected. so required number of ways $={(p+1)}^n-1$