Question

A library has $a$ copies of one book, $b$ copies of each of two books, $c$ copies of each of three books, and single copies of $d$ books. In how many ways can these books be distributed, if all are out at once?

Answer 1

We want to distribute $(a+2b+3c+d)$ books where one book has $a$ copies, 2 books has $b$ copies and 3 books has $c$ copies.

$\therefore$ The number of distributions $=\frac{(a+2b+3c+d)!}{a!(b!{)}^2(c!{)}^3}$