Question

The nine digits from 1 to 9 are used to generate a five-digit number where repetition of digits are not allowed. Find the number of possible numbers generated such that

1. there are no restrictions,
2. the number must be $1$,
3. the number must be $2$,
4. the number must be $1$ and $2$,
5. the number must be $1$ or $2$ (or both),
6. the number must be $1$ or $2$ (but not both),

Repeat parts (i)-(iv) if repitition of digits are allowed.

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