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Solving Permutations using Factorial Notation We are now going to look at situations where the number of arrangements of r objects that you can get out of n objects. Example 1: Jaden wants to choose a PIN number for his bank card. It needs to be four digits long. Each digit can be any number from 0 to 9, but he does not want any repeat any digits. How many different PIN numbers are there? Solution: Example 2: Using factorial notation to find the number of ordered tripets that can be formed from a set of eight elements. This question is asking three elements that can be chosen from eight elements or another way to look at it is how many permutations of three elements from a set of eight. Example 3: Some additional examples in shorter forms: P(17,12) = ___________________________________________________________ P(8,3) = _____________________________________________________________ P(21,5) = ____________________________________________________________ More complex Problems What if there are some restrictions on the arrangements of objects in a permutation? Example 4: In how many different ways can five different books be arranged on a shelf, if two specific books must always remain together? Hint think of the two books that need to be together as one book. Using Permutations to Determine Probability: Example 5: Four people are required to help out at party: one to prepare the food, one to serve it, one to clear the tables, and one to wash up. Determine the probability that Helena and her three siblings will be chosen for these jobs if four people are randomly selected from a room of 12 people. Solution: