Question

How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are allowed?

Answer 1

Three-digit number is to be formed from the digits 0, 1, 3, 5, 6
When repetition of digits is allowed:
100’s place digit should be a non zero number.
Hence, it can be anyone from digits 1, 3, 5, 6
∴ 100's place digit can be selected in 4 ways.
0 can appear in 10's and the unit’s place and digits can be repeated.
∴ 10's place digit can be selected in 5 ways and the unit's place digit can be selected in 5 ways
∴ By using the fundamental principle of multiplication, the total number of three-digit numbers = 4 × 5 × 5 = 100