Unit 7 Section 1 Probability Counting Techniques OBJECTIVES

Unit 7 – Section 1 “Probability. Counting Techniques” OBJECTIVES THE STUDENTS WILL BE ABLE TO CALCULATE PERMUTATIONS AND COMBINATIONS. THE STUDENT WILL BE ABLE TO USE DIFFERENT COUNTING TECHNIQUES TO DETERMINE PROBABILITY OF DIFFERENT EVENTS.

Fundamental Counting Principle can be used determine the number of possible outcomes when there are two or more characteristics. Directions: Answer the following word problem using the fundamental counting principle. Example: A student is to roll a die and flip a coin. How many possible outcomes will there be? 1. 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? 1 H 2 H 3 H 4 H 5 H 6 H 1 T 2 T 3 T 4 T 5 T 6 T 2. How many ways can you pick a sandwich by picking 1 from 3 meats, 6 veggies, 4 cheeses and 2 types of bread? 3. The letters r, s, t, v, w are to be used to form 5 -letter passwords. How many passwords can be used if the letters can be used more than once? 12 outcomes 6*2 = 12 outcomes

Permutations � Example: The number of ways to arrange the letters ABC: Number of choices for first blank? Number of choices for second blank? Number of choices for third blank? 3*2*1 = 6 3! = 3*2*1 = 6 ABC CBA ACB BAC BCA CAB Example: 1. 6 students are doing a gift exchange. How many ways can they exchange gifts? ( Can't get your own gift). 2. How many different arrangements can be made with the letters from the word MOVE?

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? � How many 4 -letter codes can be made if no letter can be used twice? � A zip code contains 5 digits. How many different zip codes can be made with the digits 0– 9 if no digit is used more than once and the first digit is not 0?

Combinations � A Combination is an arrangement of items in which order does not matter. � ORDER DOES NOT MATTER! � Words associated with Combination: Directions: Answer the following word problem using the Combination formula. 1. 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? 2. 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? 3. A student must answer 3 out of 5 essay questions on a test. In how many different ways can the student select the questions? Select Choose At random � Combinations are when you don’t care about the order, you just want to find a group of a certain size. Packing shirts for a trip, working together on a project, picking students to go on a field trip.

Permutation or Combination? Directions: Determine whether each situation involves a permutation or a combination. 1. A classroom seating chart 2. Finding the diagonals of a polygon 3. The batting order of the Denver Rockies 4. 10 books on a library shelf. 5. A hand of five cards from a deck of 52 cards. 6. A seven-person committee from your class. 7. First, second, and third chairs for six clarinets in a band. 8. Six outfits chosen from fourteen outfits to be modeled.

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