JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Permutations and Combinations

A six-digit number must use all five odd digits $1,3,5,7,9$ with exactly one of them appearing twice. Choose the repeated digit in $\left(\genfrac{}{}{0ex}{}{5}{1}\right)=5$ ways, then arrange the six digits — one of them doubled — in $\frac{6!}{2!}$ ways. The total is $5\cdot \frac{6!}{2!}=\frac{5}{2}(6!)$.