QJEEM23Ma7c31: JEE Main 2023 Mathematics - Class 11 JEEM23Ma7c31 Solution: Total numbers of 3-digit numbers that are divisible by 6 and…

A number is divisible by 6 if it is divisible by both 2 and 3. A number is divisible by 2 if its last digit is even, which means it must be either 2 or 4 from the given digits. A number is divisible by 3 if the sum of its digits is divisible by 3.

$\begin{aligned}& (2,1,3),(2,3,4),(2,5,5),(2,2,5),(2,2,2) \\\\& (4,1,1),(4,4,1),(4,4,4),(4,3,5) \\\\& 2,1,3 \Rightarrow 312,132 \\\\& 2,3,4 \Rightarrow 342,432,234,324 \\\\& 2,5,5 \Rightarrow 552 \\\\& 2,2,5 \Rightarrow 252,522 \\\\& 2,2,2 \Rightarrow 222 \\\\& 4,1,1 \Rightarrow 114 \\\\& 4,4,1 \Rightarrow 414,144 \\\\& 4,4,4 \Rightarrow 444 \\\\& 4,3,5 \Rightarrow 354,534\end{aligned}$

Total 16 numbers.