How many 3-digit numbers can be formed using the digits 2, 3, 5, 7, 8 and 9, if no digit is repeated in a number?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 120
Without repetition each place has one digit fewer than the place before it.
Hundreds place: 6 choices; tens place: 5; units place: 4
Numbers \(=6\times5\times4=\,^6P_3=120\)
Why the other options are incorrect
Option (1) 216 — Incorrect. This is \(6^3\), which allows a digit to be repeated.
Option (2) 20 — Incorrect. This is \(^6C_3\), which picks 3 digits but ignores their order.
Option (3) 720 — Incorrect. This is \(6!\), which uses all 6 digits instead of 3.