CAT 2022 Slot 1 QA Question 13: The number of ways of distributing $20$ identical balloons among $4$ children such that each child gets some balloons but no child gets an odd number of balloons, is

Question

The number of ways of distributing $20$ identical balloons among $4$ children such that each child gets some balloons but no child gets an odd number of balloons, is

Accepted Answer

Each child must receive a positive even number of balloons.
Let the four children receive $2a, 2b, 2c$ and $2d$ balloons respectively, where $a, b, c$ and $d$ are positive integers.
$2a + 2b + 2c + 2d = 20$
$\Rightarrow a+b+c+d = 10$
The number of positive integer solutions is
${}^{9}C_3 = 84$
Answe

The number of ways of distributing 202020 identical balloons among 444 children such that each child gets some balloons but no child gets an odd number of balloons, is

The number of ways of distributing $20$ identical balloons among $4$ children such that each child gets some balloons but no child gets an odd number of balloons, is