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As there are 4 numbers and they are all different, they can be arranged in:

4 choices for first number, leaving

3 choices for the second number for each choice of the first, leaving

2 choices for the third number for each of the choices of the first two, leaving

1 choice for the last number for each of the choices for the first three

giving:

number of choices = 4 x 3 x 2 x 1 = 24 possible orders in total.

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