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Bell Ringer

Bell Ringer. Samson wants to climb a mountain. He knows that if the slope is over 2, he will fall. Will he fall?. No! I’m falling!. 9 – 0 9 – 5. 9 4. =. m =. (5, 9). m = 2.25 Samson will fall!. (1, 0). Homework. 72 1680 210 5040 95,040 156. 28 10 35 20 126 220.

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Bell Ringer

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  1. Bell Ringer • Samson wants to climb a mountain. He knows that if the slope is over 2, he will fall. Will he fall? No! I’m falling! 9 – 0 9 – 5 9 4 = m = (5, 9) m = 2.25 Samson will fall! (1, 0)

  2. Homework • 72 • 1680 • 210 • 5040 • 95,040 • 156 • 28 • 10 • 35 • 20 • 126 • 220 • 792 • 1320

  3. Simple Counting Techniques

  4. Combinations (Formula) (Order doesn’t matter! AB is the same as BA) nCr = Where: n = number of things you can choose from r = number you are choosing n! r! (n – r)!

  5. Combinations • The summer Olympic games had 16 countries qualify to compete in soccer. In how many different ways can teams of 2 be selected to play each other? nCr = = = 120 different ways! 16! 2! (16 – 2)! 16•15•14•13•12•11•10•9•8•7•6•5•4•3•2•1 2•1 (14•13•12•11•10•9•8•7•6•5•4•3•2•1)

  6. Permutations (Formula) (Order does matter! AB is different from BA) nPr = Where: n = number of things you can choose from r = number you are choosing n! (n – r)!

  7. Permutations In the NBA, 8 teams from each conference make the playoffs. They are ranked by their records. If there are 15 teams in the Eastern Conference, how many different ways can they be ordered? 15P8 = = = 259,459,200 ways to order the teams! 15! (15 – 8)! 15•14•13•12•11•10•9•8•7•6•5•4•3•2•1 7•6•5•4•3•2•1

  8. Combination or Permutation? • You choose 3 toppings from 8 possible choices for your pizza. Combination, 56 different pizzas • Judges choose the first and second place winners from 12 projects. Permutation, 132 ways to choose • In a class of 22, 3 students will be chosen to go on a field trip. Combination, 1540 ways to choose

  9. Fundamental Counting Principle

  10. Fundamental Counting Principle • Independent Events – Two or more events whose outcomes have no effect on each other. • The counting principle is used to determine the number of possible outcomes for sequence of independent events. • We are not finding probability, we are simply finding how many different outcomes are possible!

  11. Fundamental Counting Principle • If we have two events (E1 & E2), where E1 can happen n1 different ways and E2 can happen n2 different ways. • The total number of outcomes for these events to occur is n1 • n2. • If we have more than two events, we continue to multiply the number of outcomes to find the total possible outcomes: n1 • n2 • n3 … • SO WE MULTIPLY THE OUTCOMES…

  12. Fundamental Counting Principle • A coin is tossed and a six-sided die is rolled. Find the number of outcomes for the sequence of events. A coin has 2 outcomes: Heads or Tails A die has 6 outcomes: 1, 2, 3, 4, 5, or 6 2 • 6 = 12 outcomes

  13. Fundamental Counting Principle For vacation, Ashley packed 5 shirts, 4 pants, and 2 pairs of shoes. How many possible outfits can Angela Create? 5 • 4 • 2 = 40 outcomes At Fake University there are 5 science, 6 social studies, 4 math, and 7 English classes to choose from. How many possible schedules could you create? 5 • 6 • 4 • 7 = 840 schedules

  14. Coin Example • How many possible outcomes are there if 6 coins are tossed? 2 • 2 • 2 • 2 • 2 • 2 = 64 outcomes • How many possible outcomes are there if 10 coins are tossed? 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2 = 1024 outcomes

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