Question

How many numbers are there between 100 and 1000 in which all the digits are distinct?

• A. 548
• B. 648
• C. 748
• D. 756

Answer 1

The correct option is B 648

Any number between 100 and 1000 is of three digits. Since the numbers should have distinct digits, repetition of digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is not allowed.

Also 0 cannot be placed on the extreme left place. Hundredth place can be filled in 9 ways. Tenth place can be filled in 9 ways. Unit's place can be filled in 8 ways.

$\therefore$ The total three-digit numbers
$=9\times 9\times 8=648$