Questions and answers

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:

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:

by Anil Sharma -
Number of replies: 0
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:

SOLUTION

Given that each child gets some balloons and an even number of balloons. Let the number of balloons are \((2a + 2),\,(2b + 2),\,(2c + 2)\) and \((2d + 2)\), where

\(2a + 2 + 2b + 2 + 2c + 2 + 2d + 2 = 20\)
\( \Rightarrow a + b + c + d = 6\)
Here \(a,\,b,\,c,\,d\) are non-negative integers, the number of solutions is \(^{6 + 4 - 1}{{\rm{C}}_{4 - 1}} = {\,^{\rm{9}}}{{\rm{C}}_{\rm{3}}} = 84\)