Question

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

Answer 1

Out of ${}^{\prime }{r}^{\prime }$ similar things, number of ways of selection is $r+1$
$\therefore$ Number of selection from ${}^{\prime }{p}^{\prime }$ copies
$=p+1$
So, for ${}^{\prime }{n}^{\prime }$ different books, number of selections $=(p+1)(p+1)(p+1).....n$ times.
$={(p+1)}^n$
Since, one blank selection is also included. Hence, Number of selections possible is
${(p+1)}^n-1$