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 _______.

Step-by-step solution

To find total numbers between 1000 and 3000 divisible by 4 using the digits 1 , 2 , 3 , 4 , 5 , 6 , We will solve in two cases. Case I : When first digit is 1 . Then last two digits can be 24 , 32 , 36 , 52 , 56 or 64 So, total ways of choosing last two digit is 6 and second digit will be chosen in 3 ways So, number of such numbers = 6 × 3 = 18 Case II: When first digit is 2 Then last two digits can be 16 , 36 , 56 or 64 So, total ways of choosing last two digit is 4 and second digit will be chosen in 3 So, nu