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JEE 2023 Mathematics PYQ — The total number of three-digit numbers, divisible by 3, which ca… | Mathem Solvex | Mathem Solvex

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1, 3, 5, 8, if repetition of digits is allowed, is:

Choose the correct answer:

A.
21
B.
18
C.
20
D.
22
(Correct Answer)

Correct Answer:

Explanation

Given digits are $1, 3, 5, 8$

Now, if 3-digit number is divisible 3, then possible triplets are $(1, 1, 1), (3, 3, 3), (5, 5, 5), (8, 8, 8), (5, 5, 8), (8, 8, 5), (1, 3, 5), (1, 3, 8)$

Hence, total numbers are

= 1 + 1 + 1 + 1 + \frac{3!}{2!} + \frac{3!}{2!} + 3! + 3!

= 4 + 3 + 3 + 6 + 6 = 22

Explanation

Given digits are $1, 3, 5, 8$

Now, if 3-digit number is divisible 3, then possible triplets are $(1, 1, 1), (3, 3, 3), (5, 5, 5), (8, 8, 8), (5, 5, 8), (8, 8, 5), (1, 3, 5), (1, 3, 8)$

Hence, total numbers are

= 1 + 1 + 1 + 1 + \frac{3!}{2!} + \frac{3!}{2!} + 3! + 3!

= 4 + 3 + 3 + 6 + 6 = 22

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