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## 11-6 6 th grade math

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**11-66th grade math**Permutations and Combinations**Objective**• To count the number of ways to choose things when order does and does not matter • Why? To know how to count arrangements when order matters (permutations)and when order does not matter (combinations).**California State Standards**SDP 3.1 : Represent all possible outcomes of compound events in an organized way (e.g., … grids, tree diagram) … MR 2.4: Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.**Vocabulary**• Permutation • Each possible arrangement of the outcomes of an event where order is important. Will be a bigger number than a combination. • To solve: multiply using factorial product of how many ways. The answer is the number of possibilities. The factorial product = x! • Who will be president and who will be treasurer • 23 students; (23 students, – 1 other student = 22) • 23 x 22 = 506 permutations To remember is permutation: Think of a perm in your hair. Ordering the way the hairdresser puts a perm in your hair is very important. Combination • Each possible arrangement of the outcomes of an event where order is not important. Will be a smaller number than a permutation. • To solve: permutation ÷ number in the combo • Two people wanting to be president/treasurer • 506/2 = 253 combinations • Ways to choose a class treasurer after president is chosen Think of the ways you can comb your hair. The order in which your comb your hair really does not matter.**How to Solve Permutations**1) Read problem. Be sure order does matter (permutation). 2) Multiply the factorial product by number of arrangements needed. 3) Multiply carefully Put 2 different-colored balloons on display. 5 Colors: red, blue, yellow, green, orange. How many different arrangements? Order matters, don’t repeat same 2 colors. 5! by 2 spaces 5 x 4 = 20 different arrangements**How to Solve Combinations**1) Read problem. Be sure order does NOT matter (= combination). 2) Divide the permutation by the number in the combo 3) Divide carefully Find the number of arrangements to make if put in 2 different colored balloons and order of arrangement does not matter. Permutation = 5 x 4 = 20 # in combo = 2 colors 20/2 = 10 choices or arrangements**Try It!**#1 & 2) Decide whether or not order matters in each situation. • Choosing 5 CD’s from a list of 20 • Choosing 5 digits for a password • How many 3-letter permutations can be made from the letters GREAT? • 4 kinds of fruit. Put 3 kinds in a basket. How many specific arrangements (permutations)? • Order not matter • Order does matter • 5! By 3 spaces = 5 x 4 x 3 = 60 permutations 4) 4! By 3 spaces = 4 x 3 x 2 = 24 arrangements**Objective Review**• To count the number of ways to choose things when order does and does not matter • Why? You now know how to count arrangements when order matters (permutations)and when order does not matter (combinations).**Independent Practice**• Complete problems 5-11 • Copy original problem first. • Show all work! • If time, complete Mixed Review: 12-15 • If still more time, work on Accelerated Math.