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Combinations

Combinations. Combinations. Objectives : (1) Students will be able to use combinations to find all possible arrangements involving a limited number of choices. Essential Questions : (1) What are combinations and how can we find them?. Combinations. What is a Combination ?

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Combinations

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  1. Combinations

  2. Combinations Objectives: (1) Students will be able to use combinations to find all possible arrangements involving a limited number of choices. Essential Questions: (1) What are combinations and how can we find them?

  3. Combinations What is a Combination? - Have you ever played a sport and thought about how many different ways the coach could have assigned players to the starting lineup? - A COMBINATION is an arrangement or listing in which order IS NOT important.

  4. Combinations How Do I Find The Value of A Combination? - We calculate the value of a combination in the following way: C(5,3) =

  5. Combinations How Do I Find The Value of A Combination? - We calculate the value of a combination in the following way: 5 x 4 x 360 3 x 2 x 1 6 Start with this number C(5,3) = = = 10 Count down this many numbers

  6. Combinations Real World Example: If Coach Bob McKillop has 12 basketball players on his team, how many ways can he choose 5 players to start a game?

  7. Combinations Real World Example: If Coach Bob McKillop has 12 basketball players on his team, how many ways can he choose 5 players to start a game? P(12,5) 12x11x10x9x8 5! 5x4x3x2x1 95040 120 C(12,5) = = = = 792 ways

  8. Combinations Example 1:Combinations. Find the value of C(6,3).

  9. Combinations Example 1:Combinations. Find the value of C(6,3). P(6,3) 6 x 5 x 4 120 3! 3 x 2 x 1 6 C(6,3) = = = = 20

  10. Combinations Example 2:Combinations. Find the value of C(15,2).

  11. Combinations Example 2:Combinations. Find the value of C(15,2). P(15,2) 15 x 14 210 2! 2 x 1 2 C(15,2) = = = = 105

  12. Combinations Example 3:Election Candidates. How many ways can a delegation of 4 people be selected from a class of 22 students?

  13. Combinations Example 3:Election Candidates. How many ways can a delegation of 4 people be selected from a class of 22 students? P(22,4) 22x21x20x19 4! 4x3x2x1 175,560 24 C(22,4) = = = = = 7315 ways

  14. Combinations Example 4:Birthday Party. Sommer is having a birthday party. She has narrowed the list to 9 people, but she can only take 4. How many combinations of friends are possible?

  15. Combinations Example 4:Birthday Party. Sommer is having a birthday party. She has narrowed the list to 9 people, but she can only take 4. How many combinations of friends are possible? P(9,4) 9x8x7x6 3024 4! 4x3x2x1 24 C(9,4) = = = = 126 ways

  16. Combinations Real World Example:Taste Test. A taste test of 9 different soft drinks is held at Ferndale. If each taster is randomly given 5 of the drinks to taste, how many combinations of soft drinks are possible?

  17. Combinations Real World Example:Taste Test. A taste test of 9 different soft drinks is held at Ferndale. If each taster is randomly given 5 of the drinks to taste, how many combinations of soft drinks are possible? P(9,5) 9x8x7x6 x515120 5! 5x4x3x2x1 120 C(9,5) = = = = 126 ways

  18. Combinations Guided Practice:Find the value. (1) C(8,3) = ? (2) How many three card hands can be dealt from a deck of 52 cards?

  19. Combinations Guided Practice:Find the value. (1) C(8,3) = 56 (2) How many three card hands can be dealt from a deck of 52 cards? 22,100 different ways

  20. Combinations Independent Practice:Find the value. (1) C(6,4) = ? (2) How many ways can you choose four items from a Chinese menu of 14 items?

  21. Combinations Independent Practice:Find the value. (1) C(6,4) = 15 (2) How many ways can you choose four items from a Chinese menu of 14 items? 1001 different ways

  22. Combinations Real World Example:Quiz Questions. On a English quiz you are allowed to answer 4 out of the 6 six questions. How many ways can you choose the questions?

  23. Combinations Real World Example:Quiz Questions. On a English quiz you are allowed to answer 4 out of the 6 six questions. How many ways can you choose the questions? P(6,4) 6x5x4x3360 4! 4x3x2x1 24 C(6,4) = = = = 15 ways

  24. Combinations Summary: - Combinations involve arrangements or listings where order is not important. - We use the following notation: C(9,4) = * The symbol C(9,4) represents the number of combinations of 9 possible things to take, and we are taking 4 of them

  25. Combinations Summary: - Combinations involve arrangements or listings where order is not important. - We use the following notation: C(9,4) = = Start with this number 9 x 8 x 7 x 6 9 x 8 x 7 x 6 4! 4 x 3 x 2 x 1 Combination Count down this many numbers = 126

  26. Combinations Homework:

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