Question

What is
is the total
number of ways in
which 5 identical
books
can
be
distributed among 3
friends
such
that
each of them gets at
least one book?​

Answer 1

Now of entries, n = 5

No. of slots, r = 3

Therefore,

no. of ways

$= \frac{n!}{(n - r)!} \\ \\ = \frac{5!}{(5 - 3)!} \\ \\ = \frac{5!}{2!} \\ \\ = \frac{5 \times 4 \times 3 \times 2!}{2!} \\ \\ = \frac{5 \times 4 \times 3 \times \cancel{2!}}{ \cancel{2!}} \\ \\ = 5 \times 4 \times 3 \\ \\ = 60$