JEE Main 2022 (Online) 28th June Morning ShiftQuestion 1
The total number of $5$-digit numbers, formed by using the digits $1,2,3,5,6,7$ without repetition, which are multiple of $6$, is
Permutation and Combination
Solution
Need even and digit sum divisible by 3. The six digits sum to 24, so the omitted digit must be a multiple of 3: omit 3 or 6. Omit 3: digits $1,2,5,6,7$, last digit 2 or 6: $2\cdot4!=48$. Omit 6: digits $1,2,3,5,7$, last digit 2: $4!=24$. Total $72$. Option (D).