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[JEE Advanced 1989] A five-digit number divisible by $3$ is formed using $0,1,2,3,4,5$ without repetition. The number of ways is

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A five-digit number divisible by $3$ is formed using $0,1,2,3,4,5$ without repetition. The number of ways is

(a) $216$
(b) $240$
(c) $600$
(d) $3125$

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 1mo ago ▲ 0

Correct answer: (a) $216$

Digit sum $15$; drop a digit $\equiv0\pmod3$ (i.e. $0$ or $3$). Drop $0$: $5!=120$; drop $3$: $5!-4!=96$. Total $216$.

JEE Advanced 1989 · Permutations and Combinations — verified solution by the Vidaara Team.

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