Question

Numbers ≥ 1000 but ≤ 4000 are formed using digits '0,1,2,3,4' . How many numbers can be formed (repetition allowed)?

Answer 1

The smallest number in the series is 1000, a 4-digit number.

The largest number in the series is 4000, the only 4-digit number to start with 4.

The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.
The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.

Hence, there are 3 * 5 * 5 * 5 or 375 numbers from 1000 to 3999.
Including 4000, there will be 376 such numbers.