How many 3-digit numbers can be formed using the digits 0, 1, 3, 5, 7 and 9, if no digit is repeated in a number?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 100
A 3-digit number cannot begin with 0, so the hundreds place is filled first.
Hundreds place: any digit except 0, so 5 choices
Tens place: the 5 digits left (0 is now allowed), so 5 choices
Units place: 4 digits left, so 4 choices
Numbers \(=5\times5\times4=100\)
Why the other options are incorrect
Option (1) 120 — Incorrect. This is \(^6P_3=6\times5\times4\); it includes the 20 “numbers” that begin with 0.
Option (3) 180 — Incorrect. This is \(5\times6\times6\), the count when digits may be repeated.
Option (4) 80 — Incorrect. This is \(5\times4\times4\), which wrongly keeps 0 out of the tens place too.