How many 3-digits even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

Question

Philoid · Accepted Answer

Let the 3-digit number be ABC, where C is at the unit’s place, B at the tens place and A at the hundreds place.

As the number has to even, the digits possible at C are 2 or 4 or 6. That is number of possible digits at C is 3. Now, as the repetition is allowed, the digits possible at B is 6 (any of the 6 is okay). Similarly, at A, also, the number of digits possible is 6.

Therefore, The total number possible 3 digit numbers =6 × 6 × 3 = 108.