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How many 6-digit numbers can be formed using only the digits 1, 3, 5, 7, and 9, with each of these digits appearing at least once and no other digit used?

1. 1/2 (6!)
2. 6!
3. 5⁶
4. 5/2 (6!)

Correct answer: 5/2 (6!)

Solution

The correct option is derived from the principle of counting arrangements of the digits while ensuring each digit appears at least once. By using the formula for permutations with restrictions, we find that the total arrangements of 6 digits, where each of the 5 digits must appear at least once, leads to the result of 5/2 (6!).

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