Question

How many integers greater than 999 but not greater than 4000 can be formed with the digits 0, 1, 2, 3 and 4 if repetition of digits is allowed?

(a) 499

(b) 500

(c) 375

(d) 376

Answer 1

Correct option is (d) 376

The smallest number in the required series is 1000 and the greatest is 4000. (The only number to start with 4)

∴ The thousands’ place can be filled with any of the 3-digits 1, 2 and 3. The next three places (hundred’s, ten’s and unit’s place) can ake any of the five values 0 or 1 or 2 or 3 or 4.

∴ Number of numbers from 100 to 3999 = 3 × 5 × 5 × 5 = 375

As 4000 is also included, so required number = 376.