Given the digits $1$ to $5$, how many odd numbers can we make?

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The digits \(1\), \(2\), \(3\), \(4\), \(5\) are written down at random to form a five-digit number.

Note; no digit may be repeated!

Find:

1. how many such numbers are possible,
2. the chance that the last digit is odd,
3. how many of the numbers are divisible by 4.