How many numbers of 3 digits can be formed with the digits 1,2,3,4,5,6 if,
(i) repetition of digits is allowed?
(ii) repetition of digits is not allowed?

Answer

To solve the problem, we will analyze both cases separately: when repetition of digits is allowed and when it is not allowed.

### Case (i): Repetition of digits is allowed

1. **Identify the number of digits available**: We have the digits 1, 2, 3, 4, 5, and 6. This gives us a total of 6 digits.

2. **Determine the number of choices for each digit**: Since repetition is allowed, each of the three positions in the three-digit number can be filled with any of the 6 digits.

3. **Calculate the total combinations**:
- For the first digit, we have 6 choices.
- For the second digit, we again have 6 choices (since repetition is allowed).
- For the third digit, we also have 6 choices.

Therefore, the total number of three-digit numbers that can be formed is:
\[ 6 \times 6 \times 6 = 6^3 = 216 \]

### Case (ii): Repetition of digits is not allowed

1. **Identify the number of digits available**: Again, we have the digits 1, 2, 3, 4, 5, and 6, which gives us a total of 6 digits.

2. **Determine the number of choices for each digit**: Since repetition is not allowed, the choices for each position will decrease as we fill in the digits.

3. **Calculate the total combinations**:
- For the first digit, we have 6 choices (any of the 6 digits).
- For the second digit, we can only choose from the remaining 5 digits (since one digit has already been used).
- For the third digit, we can only choose from the remaining 4 digits (since two digits have already been used).

Therefore, the total number of three-digit numbers that can be formed is:
\[ 6 \times 5 \times 4 = 120 \]

### Final Answers:
- For case (i), the total number of three-digit numbers formed with repetition allowed is **216**.
- For case (ii), the total number of three-digit numbers formed without repetition is **120**.