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There is a choice of 12 for the first, leaving

11 for the second, leaving

10 for the third, and so on, leaving

4 for the last, a total of 12 × 11 × 10 × ... × 4 = 79,833,600 ways.

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This is a mathematical "permutation" which is a selection of r items from a total of n items where the order of selection matters. It can be calculated by using the formula:

nPr = n!/(n-r)!

Where n! is n factorial which is calculated as n × (n-1) × (n-2) × ... 1

0! is defined to be: 0! = 1.

In this case 12P9 = 12!/(12-9)! = 12!/3! = (12 × 10 × 9 × ... × 4 × 3 × 2 × 1)/(3 × 2 × 1) = 12 × 10 × 9 × ... × 4 = 79,833,600 as before.

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8y ago

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