The number of numbers between 2000 and 5000 that can be formed with the digits 0,1 , 2, 3, 4 (repetition of digits not allowed) and are multiple of 3 is

Step-by-step solution

Number between 2000 and 5000 is a 4 digits number. For the multiples of 3, the sum of digit must be divisible by 3 . There are only 2 ways of selecting the digits so that 4 digit number with the given digits can be formed, i.e. 0, 1, 2, 3 and 0, 2, 3, 4 . The number of ways of forming number with digit 0,1,2,3 is 2 3 ! [ 0 and 1 cannot be place on thousand place] The number of ways of forming number with the digit 0,2,3,4 is 3 3 ! [ 0 cannot be place on thousand digit] Hence, the required number of ways aligned & =