Total number of numbers formed with digits 0, 1, 2, 3, 4 and 5 (without repetition) =5×5×4×3=300.
Numbers divisible by 9 ⇒ Sum of digits = 9.
Among the digits, following combination will give sum of digits = 9 ⇒0, 1, 3, 5 (since repetition not allowed and 4-digit numbers have to be formed); 0, 2, 3, 4.
With combination of 0, 1, 3 and 5 ⇒3×3×2×1=12.
With combination of 0, 2, 3 and 4 ⇒3×3×2×1=12.
Total number of numbers = 24.
Since there are 24 numbers which are divisible by 9 with the digits mentioned and without repetition, hence there will be 24 numbers which will leave remainder of 1 when divided by 9.
Hence Probability =24300=450.