How many numbers lying between 100 and 1000 can be formed with the digits 0,1,2,3,4,5 if the repetition of the digits is not allowed?

Correct option is B

Given
Digits available = {0, 1, 2, 3, 4, 5} (Total 6 digits)
Target range = 100 to 1000 (3-digit numbers)

Formula Used
Permutation principle.

Solution
A 3-digit number has places H T U.
H place (hundreds) can be filled by 5 ways (1,2,3,4,5 - cannot be 0).
T place (tens) can be filled by 5 ways (0 + remaining 4 digits).
U place (units) can be filled by 4 ways (remaining 4 digits).
Total numbers =$$5 \times 5 \times 4$$​ = 100

Final Answer
So the correct answer is (b)