JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Permutations and Combinations

The digits of $123412341$ are three $1$'s, two $2$'s, two $3$'s and two $4$'s. The even digits $2,2,4,4$ must occupy the four even places, which can be arranged in $\frac{4!}{2!2!}=6$ ways, while the odd digits $1,1,1,3,3$ fill the five odd places in $\frac{5!}{3!2!}=10$ ways. The total number of such numbers is $6\times 10=60.$