Question

How many 3 digit numbers can be formed using the digit 2, 3, 4, 5 and 6 without repetitions? How many of these are even numbers?

Answer 1

The five given digits are 2, 3, 4, 5 and 6.

Three-digit numbers are of the form .

Here, repetition of digits is not allowed.

If the units place is filled in first, then it can be filled by any of the five given digits. Therefore, there are 5 ways of filling the units place of the three-digit number.

Then, the tens place can be filled with any of the remaining four digits and the hundreds place can be filled with any of the remaining three digits.

Thus, by the fundamental principle of counting, the number of ways in which three-digit numbers can be formed without repetition is 5 × 4 × 3 = 60.

We know that an even number ends with an even digit. Hence, the units place can be filled by 2 or 4 or 6. Then, the tens place can be filled with any of the remaining four digits and the hundreds place can be filled with any of the remaining three digits.

Thus, the number of even numbers is 3 × 4 × 3 = 36.