The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is ?

(1)    Numbers formed using 0, 1, 2, 3, 4

(2)    Lie between 2000 and 5000

(3)    Multiple of 3

Case i   using  0, 1, 2, 3

             Number of 4 digit numbers between 2000, 5000 divisible by 3 $=2\times 3!$ 

Case ii   using  0, 2, 3, 4

                Number of 4 digit number b/w 2000, 5000 divisible by 3 is $3\times 3!$

               Total number of numbers b/w 2000, 5000 divisible by  $3=2\times 3!+3\times 3!=5(3!)=30$