Question 1
How many even numbers greater than 5000 can be formed using the digit 1, 2, 4, 5, 6 if no
digit is used more than once?
Observation
The Chief Examiner reported that this question was not popular among candidates as only
few candidates who attempted it scored the full marks. Majority of the candidates scored zero.
For four digit numbers that are even, it will either end with 2, 4 or 6.
If the first digit is 5, then we have 1 × 3 × 2 × 3 = 18.
If the first digit is 6, then 1 × 3 × 2 × 2 = 12.
For five digit numbers that are even, we have 4 × 3 × 2 × 1 × 3 = 72.
Therefore, even numbers greater than 5000 = 18 + 12 + 72 = 102.