How many three digit numbers can be formed by using the digits 0,… - Vidyadip

Question

How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?

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Answer

Total number of digits = 5
We cannot have 0 at the hundred's place so, the hundred's place can be digits with any of the 4 digits 1, 3, 5 or 7, So, there are 4 ways of filling the hundred's place.
Since, the digit may be repeated in three digit numbers.
$\therefore$ Ten's place can be filled with any of the 5 digits in 5 ways.
And unit's place can be filled with any of the 5 digits in 5 ways.
Hence, the total number of required numbers = 4 × 5 × 5 = 100

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