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37. Permutations and Combinations. Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another.

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Presentation on theme: "37. Permutations and Combinations. Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another."— Presentation transcript:

1 37. Permutations and Combinations

2 Fundamental Counting Principle Fundamental Counting Principle states that if an event has m possible outcomes and another independent event has n possible outcomes, then there are m * n possible outcomes for the two events together.

3 Fundamental Counting Principle For a college interview, Robert has to choose what to wear from the following: 4 slacks, 3 shirts, 2 shoes and 5 ties. How many possible outfits does he have to choose from? 4*3*2*5 = 120 outfits

4 Permutations A Permutation is an arrangement of items in a particular order. Notice, ORDER MATTERS!

5 Permutations The number of ways to arrange the letters ABC: ____ ____ ____ Number of choices for first blank ? 3 ____ ____ 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

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

7 Permutations 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? Practice: Answer Now

8 Permutations 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? Practice:

9 Combinations 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.

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

11 Combinations

12 To play a particular card game, each player is dealt five cards from a standard deck of 52 cards. How many different hands are possible? Practice: Answer Now

13 Combinations To play a particular card game, each player is dealt five cards from a standard deck of 52 cards. How many different hands are possible? Practice:

14 Permutation or combination? 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? Practice: Answer Now

15 Permutation or combination? 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? Practice:

16 Permutation or Combination A student must answer 3 out of 5 essay questions on a test. In how many different ways can the student select the questions? Practice: Answer Now

17 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? Practice:

18 Permutation or Combination 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? Practice: Answer Now

19 Combinations 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? Practice: Center: Forwards:Guards: Thus, the number of ways to select the starting line up is 2*10*6 = 120.

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