Permutations and Combinations

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Presentation transcript:

Permutations and Combinations 11-6 6th 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 Combination 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 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 1) Read problem. Be sure order does matter (permutation). 2) Multiply the factorial product by number of arrangements needed. 3) Multiply carefully

How to Solve Combinations 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 1) Read problem. Be sure order does NOT matter (= combination). 2) Divide the permutation by the number in the combo 3) Divide carefully

Try It! 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 #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)?

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.