Correct option is (c) 600
As repetition of digits is not allowed and the six digit number has to be formed using all the 6-digits 0, 1, 2, 3, 4, 5 implies that all the six digits will be used in making the number
Sum of the 6-digits = 0 + 1 + 2 + 3 + 4 + 5 = 15
Hence any 6-digit number formed with these 6 digits will be divisible by 3.
The first place from the left can be filled with any of the non zero numbers.
Now, as we can see in the diagram given
The second place with remaining 5 numbers (including 0), the third with remaining 4, the fourth with remaining 3 and so on.
∴ Number of ways in which all the six places can be filled = Number of ways of forming the 6-digit number divisible by 3
= 5 × 5 × 4 × 3 × 2 × 1
= 600
