![]() ![]() Simply stated, this states that when considering two events, both mutually exclusive (independent), then the total number of ways to do both events is the number of ways to do the first, multiplied by the number of ways to do the second. If there are distinct ways to do, andq distinct ways to do, then in total there are ways to do both and provided and are independent. This principle is called so due to its importance to counting theory. Hence we need to introduce a rigorous and systematic method to solve these counting problems. For example, considering the number of combinations of 3 objects selected from a group of 10 distinct objects, this requires 120 different cases which of course will become quite tedious to list. This method becomes tedious though when one is dealing with larger sets of objects. To calculate the number of permutations and combinations we may of course simply list the number the different cases and then simply count the number of different cases. For example, the selection ABC is the same as the selection ACB as combinations. For example the selection ABC is different to the selection ACB as permutations.ĭefinition: A combination is a selection where the order in which the objects are selected is not important and repetition of objects is not allowed. We now look to distinguish between permutations and combinations.ĭefinition: A permutation is a selection where the order in which the objects are selected is important and repetition of objects is not allowed. Permutations and Combinations involve counting the number of different selections possible from a set of objects given certain restrictions and conditions. ![]() This topic is an introduction to counting methods used in Discrete Mathematics. ![]() 3 Permutations and the Factorial Notation. ![]()
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