JEE Main 2022 (Online) 26th July Evening ShiftQuestion 1
Numbers are to be formed between $1000$ and $3000$, which are divisible by $4$, using the digits $1,2,3,4,5$ and $6$ without repetition of digits. Then the total number of such numbers is ________.
Permutation and Combination
Answer$30$
Solution
First digit is 1 or 2; divisible by 4 requires the last two digits to form a multiple of 4 with distinct digits from 1-6: 12,16,24,32,36,52,56,64. First digit 1: endings not containing 1: 24,32,36,52,56,64 (6); the second digit is any of the remaining $6-1-2=3$ digits: $6\cdot3=18$. First digit 2: endings not containing 2: 16,36,56,64 (4); second digit: $3$ choices: $12$. Total $=18+12=30$.