Permutations and combinations

Question

The total number of 4 digits numbers whose greatest common divisor with 54 is 2,is

Answer 1

54 = 2.3³

N be the 4-digit number which should be divisible by 2 but not by 3

number of numbers divisible 2=9000/2=4500

number of numbers divisible by 6= 9000/6=1500

Required 4-digit number=number of numbers divisible 2

– number of numbers divisible by 6

=4500 - 1500 = 3000