JEE Main 2023 (Online) 30th January Morning ShiftQuestion 1
Number of $4$-digit numbers (the repetition of digits is allowed) which are made using the digits $1,2,3$ and $5$, and are divisible by $15$, is equal to ______.
Permutation and Combination
Answer$21$
Solution
Last digit $5$; the first three digits from $\{1,2,3,5\}$ must make the digit sum a multiple of $3$. Counting residues ($1\to1$, $2,5\to2$, $3\to0$) gives $21$ numbers.