Question

How many 4 digit numbers are there, when a digit may be repeated any number of times?

• A. 10⁴
• B. 3 x 4³
• C. 9 x 10³
• D. 4¹⁰

Answer 1

The correct option is C

9 x 10³

In a four digit number 0 cannot be placed at thousand's place. So thousand's place can be filled with any digit from 1 to 9.

Thus thousand's place can be filled in 9 ways.

Since repetition of digits is allowed, therefore each of the remaining 3 places can be filled in 10 ways by using the digits from 0 to 9.

Hence, the required number of numbers = 9 x 10 x 10 x 10 = 9 x10³