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Fundamental counting principle Factorials Permutations Combinations Fundamental counting principle Fundamental Counting Principal = Fancy way of describing how one would determine the number of ways a sequence of events can take place. Fundamental counting principle You are at your school cafeteria that allows you to choose a lunch meal from a set menu. You have two choices for the Main course (a hamburger or a pizza), Two choices of a drink (orange juice, apple juice) and Three choices of dessert (pie, ice cream, jello). 12 meals How many different meal combos can you select?_________ Method one: Tree diagram Lunch Hamburger Pizza Apple Orange Apple Orange Pie Pie Pie Pie Icecream Icecream Icecream Icecream Jello Jello Jello Jello Fundamental counting principle Method two: Multiply number of choices 2 x 2 x 3 = 12 meals Ex 2: No repetition During the Olympic 400m sprint, there are 6 runners. How many possible ways are there to award first, second, and third places? 1st 2nd 3rd 3 places 6 5 4 ____ x ____ x ____ = 120 different ways Fundamental counting principle Ex 3: With repetition License Plates for cars are labeled with 3 letters followed by 3 digits. (In this case, digits refer to digits 0 - 9. If a question asks for numbers, its 1 - 9 because 0 isn't really a number) How many possible plates are there? You can use the same number more than once. 26 26 26 10 10 10 ___ x ___ x ___ x ___ x ___ x ___ = 17,576,000 plates Ex 4: Account numbers for Century Oil Company consist of five digits. If the first digit cannot be a 0 or 1, how many account numbers are possible? ___ x ___ x ___ x ___ x ___ = 80,000 different account #’s 8 10 10 10 10 Factorials 5 • 4 • 3 • 2 • 1 = 5! Factorial 7!= 7 • 6 • 5 • 4 • 3 • 2 •1 = 5040 42 56 Permutations Permutations = A listing in which order IS important. Can be written as: P(6,4) or 6P4 P(6,4) Represents the number of ways 6 items can be taken 4 at a time….. Or 6 x 5 x 4 x 3 = 360 Or 6 (6-1) (6-2) (6-3) 2730 Find P(15,3) = _____ 15 x 14 x 13 Permutations - Activity Write the letters G R A P H on the top of your paper. Compose a numbered list of different 5 letter Permutations. -(not necessarily words) On the bottom of your paper write how many different permutations you have come up with. Hint: You may wish to devise a strategy or pattern for finding all of the permutations before you start. Permutations Use the same formula from section 52 to solve these WPs. Ex1. Ten people are entered in a race. If there are no ties, in how many ways can the first three places come out? 10 9 8 ___ x ___ x ___ = 720 Ex2. How many different arrangements can be made with the letters in the word LUNCH? 5! or 4 3 2 1 ___ x ___ x ___ x ___ x ___ = 120 5 Ex3. You and 8 friends go to a concert. How many different ways can you sit in the assigned seats? 9! = 362,880 Combinations Combinations = A listing in which order is NOT important. Can be written as: C(3,2) or 3C2 C(3,2) means the number of ways 3 items can be taken 2 at a time. (order does not matter) Ex. C(3,2) using the letters C A T CA CT AT n = total r = What you want Combinations n = total r = What you want 7x6 42 = 21 C(7,2) = 2x1 2 Which is not an expression for the number of ways 3 items can be selected from 5 items when order is not considered? Combinations Permutations = Order IS important 8 7 6 P(8,3) = ___ x ___ x ___ = 336 Combinations = Order does not matter C(8,3) = 56 Combinations Ex1. A college has seven instructors qualified to teach a special computer lab course which requires two instructors to be present. How many different pairs of teachers could there be? C(7,2) = 21 Ex2. A panel of judges is to consist of six women and three men. A list of potential judges includes seven women and six men. How many different panels could be created from this list? Women Men C(7,6) C(6,3) = 20 7 7*20 = 140 140 choices

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Fundamental Counting Principle, Multiplication Principle, Avogadro's Principle, Dynamic worksheets, Counting Principles, combinations and permutations, Principle Works, math games, inclusion-exclusion principle, Conditional Probability

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posted: | 7/11/2011 |

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Ppt Fundamental Counting Principle document sample

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