How many odd numbers from 700 to 999, inclusive, have distinct non-zero digits?

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Odd numbers from 700 to 799, inclusive, have distinct non-zero digits:

1 \times 7 \times 4 = 28

(unit digit can be 1, 3, 5, or 9).

Odd numbers from 800 to 899, inclusive, have distinct non-zero digits:

1 \times 7 \times 5 = 35

(unit digit can be 1, 3, 5, 7, or 9).…

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What this question tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.