Question

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

• A. 648
• B. 858
• C. 546
• D. 729

Answer 1

The correct option is A

648

Since the numbers are three digit numbers, so the hundred's place can't be filled by 0, so it can be filled by any of the digits 1,2,...,9 i.e in 9 ways. Next the ten's place can be filled by any digit out of 0,1,..9 but considering that one of them is put in the hundred's place, we are left with 9 digits. For the unit's place again we can use any of the 10 digits 0,1,...,9 but two of them would have been used up for the ten's and the hundred's place, so we are left with 8 digits, since the digits of the numbers must be distinct.

Thus using the Fundamental Principle of Counting,

We get, the total number of numbers is

9 x 9 x 8 = 81 x 8 = 648