What is a Combination? A combination is a selection of r items from a set of n items such that we don't care about the order of selection. See full list on statskingdom.com What is a permutation? A permutation is a selection of r items from a set of n items where the order we pick our items matters. See full list on statskingdom.com How many ways do we have of ordering n balls? If we have 3 balls colored red (R), green (G) and purple (P) then there are 6 different ways. We have 3 options for the first color, then 2 options for the second color and one choice for the last color. Therefore we have 3 * 2 * 1 different options or 3! For 4 balls, we have 4! different permutations available. For 5 balls we have 5! different options, etc. For n balls we have n! options. Combinations versus permutations, what's the difference? The difference is whether we care about the order. With combinations, the order does not matter. If we had to pick a sports team then the order in which we pick players does not matter. If we do care about the order then we are choosing a permutation. If instead of a sports team we looked at the results of a running race then order becomes important. We do care if we come first and our main contender comes second or vice versa, even though these would be part of the same combination. How to use the combinations and permutations calculator? Order is important: defines whether you want to use the combinations calculator (when it's not active) or the permutations calculator (when it's active). With repetitions: allows you to select combinations and permutations with repetitions (active) or without (inactive). This is relevant both the combinations calculator and the permutations calculator. Identical items: allows you to specify if your problem has some repetitions of items but not infinite replacement (active) or whether it does... See full list on statskingdom.com To use the combinations generator below, you need to fill the set (by default it consists of A, B, C, D, and E elements), and enter combination size. All combinations will be generated using a lexicographic algorithm. It's also possible to generate combinations with three items per combination. After entering one or two list of items, you will see the possible number of combinations. When selecting a specific number of combinations, it will always be a random combination. To generate permutations use the Permutation Generator. Find out how many different ways to choose items. For an in-depth explanation of the formulas please visit Combinations and Permutations.
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