The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0,1,2,5,9 , if the repetition of the digits is allowed, is _ _ _ _

Step-by-step solution

(1) all different 5, 0, 1, 9 3 = 6 ways (2) 2 alike, 2 different 5, 0, 0, 1 3 ways 5, 1, 1, 2 3 ways 5, 2, 2, 0 3 ways 5, 2, 2, 9 3 ways 5, 5, 0, 2 6 ways 5, 5, 2, 9 6 ways 5, 1, 9, 9 3 ways (3) 3 alike, 1 different 5, 5, 5, 0 3 ways 5, 5, 5, 9 3 ways (4) 2 alike, 2 other alike 5, 5, 1, 1 3 ways Total ways = 42