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 if repetition of digits is not allowed and the number must be even?
There are 60 such numbers. Fill the restricted units place first with an even digit, giving 3 choices. Then 5 digits remain for the hundreds place and 4 for the tens place, so 3 × 5 × 4 = 60.
- A60Correct
- B40
- C90
- D120
Explanation
The units digit must be 2, 4 or 6: 3 ways. The hundreds digit then has 5 remaining choices and the tens digit 4. Total = 3 × 5 × 4 = 60. Using 6×5×4 = 120 ignores the evenness condition.
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