Question

There are ${}^{\prime }{m}^{\prime }$ copies each of ${}^{\prime }{n}^{\prime }$ different books in a university library. The number of ways in which one or more than one book can be selected is

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

Answer 1

The correct option is B $(m+1{)}^n-1$

There are $m$ copies each of $n$ different books.
So, we can choose any of the $m$ books of each copy or we don't choose any of them.
So, we have $(m+1)$ choices for each of $n$ different books.
But we have to select at least one book. So we will subtract a case when none of the books got selected.
Hence, no. of ways of selecting one or more books is $\left(\begin{array}{c}(m+1)\\ 1\end{array}\right)\left(\begin{array}{c}(m+1)\\ 1\end{array}\right)\left(\begin{array}{c}(m+1)\\ 1\end{array}\right).......n$ times $-1={(m+1)}^n-1$