[JEE Main 2007] s 1 12 is partitioned into labelled sets a b c of equal size
$S=\{1,\dots,12\}$ is partitioned into labelled sets $A,B,C$ of equal size $4$. The number of ways is
(a) $\frac{12!}{(4!)^3}$
(b) $\frac{12!}{(4!)^4}$
(c) $\frac{12!}{3!(4!)^3}$
(d) $\frac{12!}{3!(4!)^4}$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 4d ago
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Correct answer: (a) $\frac{12!}{(4!)^3}$
Distinct labelled groups of size $4$: multinomial $\frac{12!}{4!\,4!\,4!}=\frac{12!}{(4!)^3}$.
JEE Main 2007 · Permutations and Combinations — verified solution by the Vidaara Team.
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