'n' digits positive integers formed such that each digit is…

Maths Permutations & Combination General Single Correct MCQ

Published on: August 13, 2026

'n' digits positive integers formed such that each digit is 1, 2, or 3. How many of these contain all three of the digits 1, 2 and 3 atleast once ?

3(n –1)

3 n – 2.2 n + 3

3 n – 3.2 n – 3

3 n – 3.2 n + 3

Text Solution

Verified by Experts

The correct answer is:

Total n-digit numbers using 1, 2 or 3 = 3n

total n-digit numbers using any two digits out of 1, 2 or 3 = 3C2 × 2 n – 6 = 3 × 2 n – 6

total n-digit numbers using only one digit of 1, 2 or 3 = 3

the numbers containing all three of the digits

1, 2 and 3 at least once = 3 n – (3 × 2 n – 6) – 3 = 3 n – 3 . 2 n + 3

──────────────────────────────────────────────────────────────────────────────────────────

Previous Question Next Question

Get practice questions, solutions, and test series in one place.

Share your experience with this question and solution.

Send your comment, doubt, correction, or feedback to admin.

What students say about this solution

No reviews yet. Be the first to write a review.