How many 3-digit numbers are there when a digit may be repeated any numbers of time?

Question

Philoid · Accepted Answer

Let Suppose 3 digit number as 3 boxes as shown below.First Box is at 100^thplace, the Second box is at 10^th place, and the Third box be at 1^st place.

1^st

2^nd

3^rd

To make a 3 digit number,

1^st box can be filled with nine numbers(1, 2, 3, 4, 5, 6, 7, 8, 9) if we include 0 in 1^st box then it become 2 digit number(i.e 010 is 2 digit number not 3 digit)

2^nd box can be filled with ten numbers(1, 2, 3, 4, 5, 6, 7, 8, 9, 0) as repetation is allowed.

Similarly 3^rd box can be filled with ten numbers(1, 2, 3, 4, 5, 6, 7, 8, 9, 0)

Total number of ways is 9 × 10 × 10 = 900