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Pennant Fever Review

Pennant Fever Review. Adam Johnson Nate Levin Ian Olsen. Unit Problem. The good guys and the bad guys each have 7 games to play. Based on each of their winning records ( .62 good guys and .6 bad guys) we must determine the chances each team has to win the pennant. Key Topics. Combinations

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Pennant Fever Review

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  1. Pennant FeverReview Adam Johnson Nate Levin Ian Olsen

  2. Unit Problem • The good guys and the bad guys each have 7 games to play. Based on each of their winning records ( .62 good guys and .6 bad guys) we must determine the chances each team has to win the pennant.

  3. Key Topics • Combinations • Permutations • Pascal’s Triangle • Factorials • Binomial Theorem

  4. Factorials • Multiplication pattern • Sign is “!” • Multiply the coefficient of “!” by every whole number below it, excluding numbers zero and below. • 4!=4*3*2*1=24

  5. Combinations • nCr • n!/(n-r)!*r! • Order doesn’t matter • Bowls of ice cream • Answer question #1 on worksheet now

  6. Question #1 • 12C1 x 7C1 x 4C1 x 5C1=? • 12x7x4x5=1680 • When r value is equal to one, the final answer of the value is equal to the n value • (12!/(12-1)!*1!)*(7!/(7-1)!*1!)*etc… • 5C1=5 • 5*4*3*2*1=120 • 120/4!=5

  7. Permutations • nPr • n!/(n-r)! • Order does matter • Cones of ice cream • Answer question #4 on worksheet now

  8. Question #4 • 22P7=? • 22!/(22-7)!=859,541,760 • 22!=1.12E21 • Answer question #2

  9. Question #2 • Explain the difference between 10P7 and 10C7 • Well P will obviously be larger as the order of the combinations matter, increasing the total number of possibilities.

  10. Question #2 (Continued) • We can see the steps that are different in the previous slide that make 10P7 and 10C7 different. • Due to the difference in order mattering or not, the final answer will change drastically.

  11. Pascal’s Triangle • Shows the binomial coefficient • Shows nCr values

  12. Binomial Theorem • Finds the coefficients of binomial • Answer question #8

  13. Question #8 • (2X+3)^5

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