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Question
How many three-digit numbers can be formed using the digits 2, 3, 4, 5, 6 if digits can be repeated?
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Solution
A 3-digit number has three places which from left to right are hundred's place, ten's place and unit's place.
Here we have to form 3-digit numbers using the digits 2, 3, 4, 5, 6.
The hundred's place can be filled in by using any one of the given 5 digits in 5 ways.
Since, repetition of digits is allowed each ten's place and unit's place can be filled in by any one of the given 5 digits in 5 ways.
∴ by fundamental principle of multiplication, the total number of 3-digit numbers
= 5 × 5 × 5
= 125.
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