. is order important?. how do you compute these? Permutations

Let’s look at an example! At a juice bar, a customer who orders a smoothie gets to choose one type of fruit and one type of yogurt. For example, customers who order a “Simple Smoothie” get to choose from 3 fruits (bananas, peaches, and blueberries) and 2 yogurts (plain or vanilla). The tree diagram shows that there are 6 possible types of Simple Smoothies: plainplainplain Banana Peach Blueberry vanillavanillavanilla

A permutation is a selection of items from a group in which the order is important. In a permutation, AB is not the same as BA. To begin, consider there are n items and you want to select r items from that group and organize them in a certain order. The mathematical formula is You may also think of this as (n)(n-1)(n-2)… multiplied r times. For instance, if there are 9 items and you want to order 3 of them, you can multiply 9x8x7 and this would give you the number of ways to order the 3 items (the factorial formula also gives the same result). Want to give this a try on your own? (click when you’re ready…) How many ways can club members select a President, a Vice President, a Secretary, and a Treasurer from a group of 10 members? Remember, order matters because each office is different…

type your answer in the Blackboard free response area for your teacher to see… (I’ll be waiting…) What’s your guess?

If you answered , you were correct! If you didn’t get that answer, no worries mate! We’ll try another one now…

“Those Pesky Passwords” Nowadays it seems you need a password to sign into every internet site. Mrs. Herr’s math website is no different; she requires a password of 5 letters, with only the capital letters A thru H being valid. Letters may not be repeated. Nowadays it seems you need a password to sign into every internet site. Mrs. Herr’s math website is no different; she requires a password of 5 letters, with only the capital letters A thru H being valid. Letters may not be repeated. How many possible passwords are there to her website?. Some valid examples are DECAH, BEACH, and FACED. Invalid entries would be DEADF (repeating D’s), HEADS (S isn’t between A and H), and ABcDe (lower case letters not permitted)

Let’s get to the answer…  There are 8 choices of letters – A, B, C, D, E, F, G, and H  There are 5 positions to be filled for the password _ _ _ _ _  You have 8 choices of letters for the 1 st position…  7 letters to pick for the 2 nd position…  6 choices for the 3 rd position, etc…  So there are 8x7x6x5x4 or 6720 possible passwords  Did you get that for your answer?

Way to go, buddy! I knew you could do it! Next, we’re off to discover COMBINATIONS

Combinations A combination is a selection of items from a group in which order is not important. AB is the same as BA; ‘xyz’ is the same as ‘xzy’, ‘yxz’, ‘yzx’, ‘zxy’, and ‘zyx’.

Here’s what a combination problem looks like: How many ways can club members select a committee of 4 people from a group containing 10 members? The order of the members does not matter… selecting Tom, Joe, Sally and Molly is the same as selecting Sally, Joe, Molly and Tom. Therefore a formula different from the permutation formula must be used. It is similar but has one key difference: (notice the r! in the denominator ~ that’s not present in the permutation formula).

Melania is married to a wealthy man who has showered her with many expensive items. Among them is a collection of 20 precious-jewel rings. Melania wants to wear 3 of these but just can’t decide which ones to select. How many groups of 3 rings does she have to choose from?

your answer here: In all of the combinations of 3 rings, order is not important…picking the sapphire, diamond, and ruby rings is the same as picking the ruby, diamond and sapphire rings. So the answer is obtained by using the combination formula: How’d you do? AWESOME!!

Thanks for your time – peace out!