# How Many 3-digit Numbers Are There, with Distinct Digits, with Each Digit Odd? - Mathematics

How many 3-digit numbers are there, with distinct digits, with each digit odd?

#### Solution

The hundred's place can be filled by {1, 3, 5, 7, 9), i.e. 5 digits.
The ten's place can now be filled by 4 digits (as one digit is already used in the hundred's place and repetition is not allowed )
Similarly, the unit's place can be filled by 3 digits.
Total number of 3-digit numbers = 5xx4xx3=60

Concept: Combination
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.2 | Q 25 | Page 15