JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Permutations and Combinations

An odd number requires its unit digit to be $1,3,$ or $5$. With unit digit $5$, the remaining $1,2,2,2,3,3$ arrange in $\frac{6!}{3!2!}=60$ ways; with unit digit $3$, the remaining $1,2,2,2,3,5$ give $\frac{6!}{3!}=120$ ways; with unit digit $1$, the remaining $2,2,2,3,3,5$ give $\frac{6!}{3!2!}=60$ ways. The total count is $60+120+60=240$.