How many 4-digit numbers greater than 4000 can be formed using the digits 2, 3, 4, 5 and 6, if no digit is repeated in a number?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 72
A 4-digit number made from these digits is greater than 4000 exactly when its first digit is 4, 5 or 6. That place is filled first, then the others from the digits left.
Thousands place: 4, 5 or 6, so 3 choices
Hundreds place: any of the 4 digits left, 4 choices
Tens place: 3 choices left
Units place: 2 choices left
Numbers \(=3\times4\times3\times2=72\)
Why the other options are incorrect
Option (1) 120 — Incorrect. This is \(5\times4\times3\times2\), all the 4-digit numbers, including those that begin with 2 or 3.
Option (2) 96 — Incorrect. This allows 4 first digits; only 4, 5 and 6 give a number above 4000.
Option (3) 48 — Incorrect. This allows only 5 and 6 first, but numbers such as 4235 that begin with 4 are also greater than 4000.