JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Permutations and Combinations

Only four- and five-digit integers can be formed, as there are five distinct digits with no repetition. A four-digit number exceeds $7000$ exactly when its leading digit is $7$ or $8$, giving $2$ choices, with the other three places filled from the remaining four digits in $4\times 3\times 2=24$ ways, so $2\times 24=48$ such numbers. Every five-digit arrangement of all five digits exceeds $7000$, contributing $5!=120$. The total count is $48+120=168$.