How many 3-digit even numbers can be formed using the digits 1, 2, 3, 5, 6 and 9, if no digit is repeated in a number?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 40
A number is even when its units digit is even. The place with the condition is filled first, then the others.
Units place: 2 or 6, that is 2 choices
Hundreds place: any of the other 5 digits; tens place: 4 left
Numbers \(=2\times5\times4=40\)
Why the other options are incorrect
Option (1) 120 — Incorrect. This is \(6\times5\times4\), all the numbers, odd ones included.
Option (3) 60 — Incorrect. This takes half of 120, but only 2 of the 6 digits are even, so even numbers are not half.
Option (4) 20 — Incorrect. This counts only one even units digit; both 2 and 6 can be used.