How many 3-digit odd numbers can be formed by using the digits 1, 2, 3, 4, 5, 6 when
(i) the repetition of digits is not allowed?
(ii) the repetition of digits is allowed?

Explanation

To solve the problem of how many 3-digit odd numbers can be formed using the digits 1, 2, 3, 4, 5, and 6, we will consider two cases:

### Case 1: Repetition of digits is not allowed

1. **Identify the digits available**: The digits we can use are 1, 2, 3, 4, 5, and 6. The odd digits among these are 1, 3, and 5.

2. **Determine the unit place**: Since we need to form an odd number, the unit place can only be filled with the odd digits (1, 3, or 5). This gives us 3 choices for the unit place.

...