How many 4-digit even numbers can be formed using the digits 1, 2, 3, 4, 5 and 6, if no digit is repeated in a number?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 180
A number is even when its units digit is even. The place with the condition is filled first, then the other places with the digits left; the choices are multiplied.
Units place: an even digit, 2, 4 or 6, so 3 choices
Thousands place: any of the 5 digits left, 5 choices
Hundreds place: 4 choices left
Tens place: 3 choices left
Numbers \(=3\times5\times4\times3=180\)
Why the other options are incorrect
Option (1) 360 — Incorrect. This is \(6\times5\times4\times3\), all the 4-digit numbers, odd ones included.
Option (3) 120 — Incorrect. This takes only 2 even digits for the units place; there are 3 (2, 4 and 6).
Option (4) 216 — Incorrect. This is \(6^3\) and does not follow the rule that no digit repeats.