Happy Pi Day! Find x. 15 If you still have x

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Permutations and Combinations

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Presentation transcript:

3-14-14 Happy Pi Day! Find x. 15 If you still have x Area of triangle worksheet LOS or LOC worksheet (sideways) I need them in the basket NOW! (Mon at the LATEST!) x 6

Project

30 min from NOW (so listen) Blank sheet of paper- name IN ORDER Work any problem you missed with ALL work. NO WORK = NO CREDIT I will only grade extra sheet of paper. Open note. BY YOURSELF!

Permutations and Combinations

Permutations Notice, ORDER MATTERS! A Permutation is an arrangement of items in a particular order. Notice, ORDER MATTERS! To find the number of Permutations of n items, we can use the Fundamental Counting Principle or factorial notation.

Permutations The number of ways to arrange the letters ABC: ____ ____ ____ 3 ____ ____ Number of choices for first blank? 3 2 ___ Number of choices for second blank? Number of choices for third blank? 3 2 1 3*2*1 = 6 3! = 3*2*1 = 6 ABC ACB BAC BCA CAB CBA

Permutations To find the number of Permutations of n items chosen r at a time, you can use the formula

Permutations Example: A combination lock will open when the right choice of three numbers (from 1 to 30, inclusive) is selected. How many different lock combinations are possible assuming no number is repeated?

Permutations Example: A combination lock will open when the right choice of three numbers (from 1 to 30, inclusive) is selected. How many different lock combinations are possible assuming no number is repeated?

Permutations Example: From a club of 24 members, a President, Vice President, Secretary, Treasurer and Historian are to be elected. In how many ways can the offices be filled?

Permutations Example: From a club of 24 members, a President, Vice President, Secretary, Treasurer and Historian are to be elected. In how many ways can the offices be filled?

Combinations ORDER DOES NOT MATTER! A Combination is an arrangement of items in which order does not matter. ORDER DOES NOT MATTER! Since the order does not matter in combinations, there are fewer combinations than permutations. The combinations are a "subset" of the permutations.

Combinations To find the number of Combinations of n items chosen r at a time, you can use the formula

Combinations To find the number of Combinations of n items chosen r at a time, you can use the formula

Combinations Example: To play dodge ball, the PE teacher needs to pick 2 dodge balls out of a bin that holds 7 dodge balls. How many different ways can the PE teacher select the dodge balls?

Combinations To play dodge ball, the PE teacher needs to pick 2 dodge balls out of a bin that holds 7 dodge balls. How many different ways can the PE teacher select the dodge balls? Example:

Combinations Example: A student must answer 3 out of 5 essay questions on a test. In how many different ways can the student select the questions?

Combinations A student must answer 3 out of 5 essay questions on a test. In how many different ways can the student select the questions? Example:

Combinations Example: A basketball team consists of two centers, five forwards, and four guards. In how many ways can the coach select a starting line up of one center, two forwards, and two guards?

Combinations Example: A basketball team consists of two centers, five forwards, and four guards. In how many ways can the coach select a starting line up of one center, two forwards, and two guards? Center: Forwards: Guards: Thus, the number of ways to select the starting line up is 2*10*6 = 120.

Homework Worksheet