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Question
How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are allowed?
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Solution
A 3-digit number has 3 places which from left to right are hundred's place, ten's place, and unit's place.
Zero cannot be in the hundred's place. Hence, hundred's place can be filled in by anyone of the 4 non-zero digits 1, 3, 5, 6. Thus hundred's places can be filled in 4 ways.
Since repetition of digits is allowed, the ten's place and unit's place can be filled by anyone of the given 5 digits i.e., ten's place and unit's place can be filled in 5 different ways each.
∴ by fundamental principle of multiplication, the total number of 3-digit numbers formed
= 4 × 5 × 5
= 100
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