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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations

How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6 without repeating any digit, such that the number is even?

There are 60 such numbers. Fill the restricted units place first with an even digit (2, 4 or 6), giving 3 ways. Then 5 digits remain for the tens place and 4 for the hundreds place, so 3 × 5 × 4 = 60.

  1. A40
  2. B60Correct
  3. C120
  4. D90

Explanation

The units digit must be 2, 4 or 6: 3 ways. The tens digit can be any of the remaining 5 digits: 5 ways. The hundreds digit then has 4 ways. Total = 3 × 5 × 4 = 60. The value 120 counts all 3-digit numbers, ignoring the even condition.

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