How many 4-digit numbers can be formed using the digits 0, 1, 2, 3 and 4, if the repetition of digits is allowed?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 500
A 4-digit number cannot begin with 0. With repetition allowed, every other place can take any of the 5 digits, 0 included.
Thousands place: 1, 2, 3 or 4, so 4 choices
Hundreds place: any of 0, 1, 2, 3, 4, so 5 choices
Tens place: 5 choices
Units place: 5 choices
Numbers \(=4\times5\times5\times5=500\)
Why the other options are incorrect
Option (2) 625 — Incorrect. This is \(5^4\), which also counts strings such as 0123 that begin with 0 and are not 4-digit numbers.
Option (3) 96 — Incorrect. This is \(4\times4\times3\times2\), the count when repetition is not allowed.
Option (4) 256 — Incorrect. This is \(4^4\), which leaves 0 out of every place; 0 can be used in the last three places.