How any three digit odd numbers can be formed by using the digits 1,2,3,4,5,6 if; The repetition of digits is not allowed? The repetition of digits is allowed?

Explanation

To solve the problem of how many three-digit odd numbers can be formed using the digits 1, 2, 3, 4, 5, and 6, we will consider two cases: when repetition of digits is not allowed and when repetition of digits is allowed.

### Case 1: Repetition of Digits is Not Allowed

1. **Identify the last digit (odd digit)**:
- The last digit of the three-digit number must be odd. The available odd digits from the set {1, 2, 3, 4, 5, 6} are 1, 3, and 5.
- Therefore, we have 3 choices for the last digit.

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