Question

How many different three digit numbers can be formed with the digits 1, 2, 3, 4, 5 and 6 so that none of the digits are repeated?

• A. 120
• B. 130
• C. 150
• D. 100
• E. 80

Answer 1

The correct option is A 120

Suppose we start with the unit’s place. Unit place can be filled by any of the 6 digits given, so it can be filled in 6 ways. Now coming the tens place, it can be filled by any of the six digits except the one which has been used at unit’s place. So, it can be filled in 5 ways. Similarly the hundred’s place can be filled by any of the six digits except those two which have been used at unit’s and tens’ place. So, it can be filled in 4 ways.

4 ways 5 ways 6 ways

So, total numbers of numbers possible = $6\times 5\times 4=120$. Hence option (a)