Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is ________ . [2023]

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Solution

Q.
Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is ________ . [2023]

Ans.
(16)

Total 3-digit numbers formed by 1, 2, 3, 4, 5 when the last digit in 4 and divisible by 6.

$\begin{matrix} 1 & 1 & \to & 1 \\ 4 & 4 & \to & 1 \\ 1 & 4 & \to & 2! \\ 2 & 3 & \to & 2! \\ 3 & 5 & \to & 2! \end{matrix}] = 8$

When last digit is 2:

$\begin{matrix} 2 & 2 & \to & 1 \\ 5 & 5 & \to & 1 \\ 1 & 3 & \to & 2! \\ 2 & 5 & \to & 2! \\ 4 & 3 & \to & 2! \end{matrix}] = 8$

$∴ Total 3-digit numbers formed by 1, 2, 3, 4, 5 which are divisible by 6 are 16 .$

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