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When the order matters and each object can be chosen only once, then the number of permutations is where n is the number of objects from which you can choose, r is the number to be chosen and "!" is the standard symbol meaning factorial. For example, if you have five people and are going to choose three out of these, you will have 5!/(5 - 3)! = 60 permutations. Note that if n = r (meaning the number of chosen elements is equal to the number of elements to choose from; five people and pick all five) then the formula becomes where 0! = 1. For example, if you have the same five people and you want to find out how many ways you may arrange them, it would be 5! or 5 × 4 × 3 × 2 × 1 = 120 ways. The reason for this is that you can choose from 5 for the initial slot, then you are left with only 4 to choose from for the second slot etc. Multiplying them together gives the total of 120. As a second, very easy, example we may want to see in how many ways we may rearrange the three letters A, B, C. Using the given above combinatorial formula for permutations without repetitions we have 3! or 3 × 2 × 1 = 6 ways. If we check the following on practice, try to rearrange the letters by hand, we have the following combinations: ABC, ACB, BCA, BAC, CAB, CBA. If, for instance, the three letters were A, A, B, then the number of combinations will be different and we would have to use a different combinatorial formula, the formula for permutations with repetitions.

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