Combinations and Permutations
What's the Difference? In English we use the word "combination" loosely, without thinking if the order of things is important. In other words: So, in Mathematics we use more precise language: In other words: A Permutation is an ordered Combination. Permutations There are basically two types of permutation: Repetition is Allowed: such as the lock above. 1. These are the easiest to calculate. When we have n things to choose from ... we have n choices each time! When choosing r of them, the permutations are: n × n × ... (In other words, there are n possibilities for the first choice, THEN there are n possibilites for the second choice, and so on, multplying each time.) Which is easier to write down using an exponent of r: n × n × ... Example: in the lock above, there are 10 numbers to choose from (0,1,...9) and we choose 3 of them: 10 × 10 × ... (3 times) = 103 = 1,000 permutations So, the formula is simply: 2. In this case, we have to reduce the number of available choices each time. Do you see? 1. 2.