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Deconstructing the Question
There are 9 distinct toys to be distributed among 4 distinct children.
“Even distribution among the 3 elder children” means the 3 elder children get the same number of toys.
The youngest gets one more toy than each elder child.

Step-by-step
Let each elder child receive \(x\) toys, so the youngest receives \(x+1\).
Total toys:
\(3x + (x+1) = 9 \Rightarrow 4x+1=9 \Rightarrow x=2\)

So the counts are:
- youngest: \(3\) toys
- each of 3 elders: \(2\) toys

Choose toys step by step:
- youngest gets 3: \(C(9,3)\)
- elder #1 gets 2 from remaining 6: \(C(6,2)\)
- elder #2 gets 2 from remaining 4: \(C(4,2)\)
- elder #3 gets last 2: \(C(2,2)=1\)

Total:
\(C(9,3)\cdot C(6,2)\cdot C(4,2)\cdot C(2,2)\)

This simplifies to:
\(\frac{9!}{3!\,2!\,2!\,2!}=\frac{9!}{3!(2!)^3}\)



Answer: (D) 9! / (3!(2!)^3)
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