Question

The number of integers greater than 6000 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

The correct option is B 192

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