Question

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

• A. 216
• B. 192
• C. 120
• D. 72

Answer 1

Answer: (B)

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 $8$ .

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 $=72+120=192$