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Transparency 5. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 5-4b. Objective. Find the number of combinations of a set of objects. Example 5-4b. Vocabulary. Combination. An arrangement, or listing, of objects in which order is not important.

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  1. Transparency 5 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 5-4b Objective Find the number of combinations of a set of objects

  4. Example 5-4b Vocabulary Combination An arrangement, or listing, of objects in which order is not important P(a, b) C(a, b) = b!

  5. Example 5-4b Vocabulary Permutation An arrangement, or listing, of objects in which order is important P(a, b) = P(a, b)

  6. Lesson 5 Contents Example 1Find the Number of Combinations Example 2Use a Combination to Solve a Problem Example 3Identify Permutations and Combinations Example 4Identify Permutations and Combinations

  7. Example 5-1a DECORATINGAda can select from seven paint colors for her room. She wants to choose two colors. How many different pairs of colors can she choose? She wants to choose 2 colors which makes this a combination C(a, b) = Write the combination statement A combination is another modified permutation and order is not important 1/4

  8. Example 5-1a DECORATINGAda can select from seven paint colors for her room. She wants to choose two colors. How many different pairs of colors can she choose? P(a, b) Write formula for combination C(a, b) = b! “a” represents the number of choices C(7, 2) = Replace a with 7 “b” represents the number wants to choose Replace b with 2 1/4

  9. Example 5-1a DECORATINGAda can select from seven paint colors for her room. She wants to choose two colors. How many different pairs of colors can she choose? P(a, b) C(a, b) = Complete the equation by replacing values for a and b b! P(7, 2) C(7, 2) = P(7, 2) is a permutation that begins with 7 and multiply only 2 numbers 2! 7  6 C(7, 2) = 2  1 Write definition of 2! 1/4

  10. Example 5-1a DECORATINGAda can select from seven paint colors for her room. She wants to choose two colors. How many different pairs of colors can she choose? P(a, b) Follow Order of Operations P E MD AS C(a, b) = b! P(7, 2) C(7, 2) = 2! Multiply in numerator 7  6 C(7, 2) = Multiply in denominator 2  1 Divide numerator by denominator 42 C(7, 2) = 2 Answer: Add dimensional analysis C(7, 2) = 21 pairs of colors 1/4

  11. Example 5-1b HOCKEY The Brownsville Badgers hockey team has 14 members. Two members of the team are to be selected to be the team’s co-captains. How many different pairs of players can be selected to be the co-captains? Answer: C(14, 2) = 91 pairs of players 1/4

  12. Example 5-2a INTRODUCTIONSTen managers attend a business meeting. Each person exchanges names with each other person once. How many introductions will there be? Write the combination formula P(a, b) C(a, b) = b! “a” represents the number of choices 2) = C(10, Replace a with 10 “b” represents the number wants to choose This represents 2 people Replace b with 2 2/4

  13. Example 5-2a INTRODUCTIONSTen managers attend a business meeting. Each person exchanges names with each other person once. How many introductions will there be? P(a, b) Complete the equation by replacing values for a and b C(a, b) = b! P(10, 2) P(10, 2) is a permutation that begins with 10 and multiply only 2 numbers 2) = C(10, 2! 10  9 C(10, 2) = 2  1 Write definition of 2! 2/4

  14. Example 5-2a INTRODUCTIONSTen managers attend a business meeting. Each person exchanges names with each other person once. How many introductions will there be? P(a, b) Follow Order of Operations P E MD AS C(a, b) = b! P(10, 2) C(10, 2) = 2! Multiply in numerator 10  9 C(10, 2) = Multiply in denominator 2  1 90 Divide numerator by denominator C(10, 2) = 2 Answer: Add dimensional analysis C(10, 2) = 45 introductions 2/4

  15. Example 5-2c PHYSICAL EDUCATIONTwelve students in a physical education class must pair off for a particular exercise. How many different pairs are possible? Answer: C(12, 2) = 66 pairs 2/4

  16. Example 5-3a TRACKFrom an eight-member track team, three members will be selected to represent the team at the state meet. How many ways can these three members be selected? Does the situation represent a permutation or a combination? Does the situation represent a permutation or a combination? Combination = order not important Permutation = order important Combination P(a, b) C(a, b) = b! Determine if order is important Order is not important because a member can be in any selection Write combination formula 3/4

  17. Example 5-3a TRACKFrom an eight-member track team, three members will be selected to represent the team at the state meet. How many ways can these three members be selected? Does the situation represent a permutation or a combination? “a” represents the number of choices Combination P(a, b) C(a, b) = Replace a with 8 b! C(8, 3) = “b” represents the number wants to choose Replace b with 3 3/4

  18. Example 5-3a TRACKFrom an eight-member track team, three members will be selected to represent the team at the state meet. How many ways can these three members be selected? Does the situation represent a permutation or a combination? Complete the equation by replacing values for a and b Combination P(a, b) C(a, b) = b! P(8, 3) is a permutation that begins with 8 and multiply 3 numbers P(8, 3) C(8, 3) = 3! 8  7  6 3  2  1 C(8, 3) = Write definition of 3! 3/4

  19. Example 5-3a Follow Order of Operations P E MD AS Combination P(a, b) Multiply in numerator C(a, b) = b! Multiply in denominator P(8, 3) C(8, 3) = 3! Divide numerator by denominator 8  7  6 3  2  1 C(8, 3) = Add dimensional analysis 336 6 C(8, 3) = How many ways can these three members be selected? Answer: C(8, 3) = 56 ways 3/4

  20. Example 5-4b * COMMITTEESIn how many ways can you choose a committee of four people from a staff of ten? Does the situation represent a permutation or a combination? Solve the problem. Answer: Combination C(10, 4) = 210 ways 3/4

  21. Example 5-4a TRACKIn how many ways can you choose the first, second, and third runners in a relay race from eight members of a track team? Does the situation represent a permutation or a combination? Combination = order not important Permutation = order important P(a, b) = P(a, b) Determine if order is important Order is important because a runner in first cannot run in second Write permutation formula 4/4

  22. Example 5-4a TRACKIn how many ways can you choose the first, second, and third runners in a relay race from eight members of a track team? Does the situation represent a permutation or a combination? “a” represents the number of choices P(a, b) = P(a, b) P(8, P(8, 3) 3) = Replace a with 8 “b” represents the number wants to choose Replace b with 3 Complete the equation by replacing values for a and b 4/4

  23. Example 5-4a TRACKIn how many ways can you choose the first, second, and third runners in a relay race from eight members of a track team? Does the situation represent a permutation or a combination? P(8, 3) is a permutation that begins with 8 and multiply 3 numbers P(a, b) = P(a, b) P(8, P(8, 3) 3) = P(8, 3) = 8  7  6 Multiply Answer: Add dimensional analysis ways P(8, 3) = 336 4/4

  24. Example 5-3b PTA There are fifteen members on the PTA for a local middle school. Three of those fifteen will be elected for the offices of president, secretary, and treasurer of the PTA. How many ways can these three positions be filled? Does the situation represent a permutation or a combination? Solve the problem. Answer: Permutation P(15, 3) = 2,730 ways 4/4

  25. End of Lesson 5 Assignment

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