Given Information:
We need to create three-digit numbers from the digits 1, 4, 5, 6, 7, and 8, and the digits can be repeated.
Column A: Three-Digit Odd Numbers
To form a three-digit odd number, the last digit (units place) must be an odd digit. From the given digits, the odd digits are 1, 5, and 7.
- Units place (odd digit): We have 3 choices (1, 5, or 7).
- Hundreds place: We can choose any of the 6 digits (1, 4, 5, 6, 7, or 8), so we have 6 choices.
- Tens place: We can again choose any of the 6 digits, so we have 6 choices.
The total number of three-digit odd numbers is:
6 × 6 × 3 = 108
Thus, Column A has 108 possible numbers.
Column B: Three-Digit Even Numbers
To form a three-digit even number, the last digit (units place) must be an even digit. From the given digits, the even digits are 4, 6, and 8.
- Units place (even digit): We have 3 choices (4, 6, or 8).
- Hundreds place: We can choose any of the 6 digits, so we have 6 choices.
- Tens place: We can again choose any of the 6 digits, so we have 6 choices.
The total number of three-digit even numbers is:
6 × 6 × 3 = 108
Thus, Column B also has 108 possible numbers.
Comparison:
- Column A has 108 ways.
- Column B has 108 ways.
Therefore, both quantities are equal.
Answer: C: Both are equal