Question

The number of numbers greater than or equal to 1000 but less than or equal to 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed) is

• A. 376
• B. 370
• C. 360
• D. 366

Answer 1

The correct option is A 376

We are given the fact that the number is greater than or equal 1000 and less than or equal 4000. So the first digit can be 1 or 2 or 3 or 4. There are 4 ways to fill the first digit.

If first digit is 1, 2 or 3, what about the next three digits? Are there any constraints on those digits when repetitions are allowed? No. So thre next three digits can be filled in five ways each.

Required number of numbers $=3\times 5\times 5\times 5=375$
if first digit is 4 then only 1 number is possible . it is 4000.
so total is 375+1=376