Question

There are $n$ different books and $p$ copies of each in a library. The number of ways in which one or more than one book can be selected is:

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

Answer 1

Answer: (B)

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

Number of ways in which one or more objects can be selected out of $S_1$ alike objects of one kind, $S_2$ alike objects of second kind and $S_3$ alike objects of third kind
=$(S_1+1)$$(S_2+1)$$(S_3+1)-1$

The above formula can be generalized as follows.

Number of ways in which one or more objects can be selected out of $S_1$ alike objects of one kind, $S_2$ alike objects of second kind , $S_3$ alike objects of third kind and so on ... $S_n$ alike objects of $n^{th}$ kind
$(S_1+1)$$(S_2+1)$$(S_3+1)$............$(S_n+1)-1$

In our case it is ${(p+1)}^n-1$