[JEE Advanced 2004] Prove that $\dfrac{(n^2)!}{(n!)^n}$ is an integer for $n\in\mathbb Z^+$.
Prove that $\dfrac{(n^2)!}{(n!)^n}$ is an integer for $n\in\mathbb Z^+$.
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· 1mo ago
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Answer: Proved.
It is the multinomial coefficient counting the partitions of $n^2$ distinct objects into $n$ ordered groups of size $n$ each — necessarily an integer.
JEE Advanced 2004 · Permutations and Combinations — verified solution by the Vidaara Team.
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