Question

Find the total number of ways to put $7$ identical apples into $4$ identical packages so that each package has at least one apple.
(correct answer + 2, wrong answer 0)

Answer 1

$7$ identical apples can be divided into four parts as $(1,2,2,2),(1,1,1,4),(1,1,2,3)$ as in three ways.
Now, since the packages are identical, these three divisions can be distributed in four packages in one way only.
$\therefore$ Total number of ways $=3\times 1=3$