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  4. The number of integers greater than 6,000 that can be formed using the digits 3, 5, 6, 7 and 8 without repetition is

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Q. The number of integers greater than $6,000$ that can be formed using the digits $3, 5, 6, 7$ and $ 8$ without repetition is

JEE MainJEE Main 2015Permutations and Combinations

Solution:

The integer greater than $6000$ may be of $4$ digits or $5$ digits. So, here two cases arise.
Case I When number is of $4$ digits.
Four-digit number can start from $6,7$ or $8$ .
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Thus, total number of $4$-digit numbers, which are greater than
$6000=3 \times 4 \times 3 \times 2=72$
Case II When number is of $5$ digits.
Total number of five-digit numbers which are greater than $6000=5$ ! $=120$
$\therefore$ Total number of integers $=72+120=192$