CAT 2021 Slot 2 QA Question 18: The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is

Question

The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is

Accepted Answer

The three distributions are independent, so count each one separately and multiply.

Balloons: each child gets at least 4. After giving 4 balloons to each child, 3 balloons remain to be distributed among 3 children.
$	ext{Number of ways} = \binom{3+3-1}{3-1}=\binom{5}{2}=10$

Pencils: each child ge