How many 3-digit numbers can be formed using only the digits 3, 5, 6, 7 and 9, if the repetition of digits is allowed?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 125
With repetition allowed, every place can take any of the digits; the choices for the places are multiplied.
Each of the 3 places has 5 choices (3, 5, 6, 7 or 9)
Numbers \(=5\times5\times5=5^3=125\)
Why the other options are incorrect
Option (1) 60 — Incorrect. This is \(5\times4\times3\), the count without repetition.
Option (2) 243 — Incorrect. This is \(3^5\); there are 5 digits for each of 3 places, so it is \(5^3\).
Option (3) 15 — Incorrect. This is \(5\times3\); the choices must be multiplied place by place.