The number of 3-digit integers that are multiple of 6 which can be formed by us…

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The number of 3-digit integers that are multiple of 6 which can be formed by using the digits 1,2,3,4,5,6 without repetition is

1
2
3
4

To be a multiple of $6$:

• last digit must be even → ${2,4,6}$

• sum of digits must be divisible by $3$.

For each even last digit, exactly 8 valid choices of the first two digits satisfy divisibility by $3$ (checked by mod – 3 pairing).

So total numbers: 3×8=24

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