JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Permutations and Combinations

A number strictly between $5000$ and $10000$ built from $1,3,5,7,9$ without repetition is a four-digit number whose leading digit must be $5$, $7$ or $9$, giving three choices. The remaining three places are filled from the four unused digits in $4\times 3\times 2=24$ ways. The total is $3\times 24=72$.