JEE Main · 2015 · 04 Apr 2015 · Offline · Permutations and Combinations

Count the numbers above $6000$ by length. A four-digit number clears $6000$ only if it starts with $6,7$ or $8$ -- three choices -- and the remaining three places are filled from the leftover digits in $4\times 3\times 2=24$ ways, giving $3\times 24=72$. Every five-digit number using all five digits already exceeds $6000$, and there are $5!=120$ of them. Altogether $72+120=192$.