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Section 11.8

Chapter 11. Section 11.8. Exercise #1. A parent teacher committee consisting of four people is to be formed from 20 parents and five teachers. Find the probability that the committee will consist of the following. (Assume that the selection will be random.). (a) All teachers

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Section 11.8

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  1. Chapter 11 Section 11.8 Exercise #1

  2. A parent teacher committee consisting of four people is to be formed from 20 parents and five teachers. Find the probability that the committee will consist of the following. (Assume that the selection will be random.)

  3. (a) All teachers (b) Two teachers and two parents (c) All parents (d) One teacher and three parents

  4. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 25! 25C4 = 4!(25 – 4)!

  5. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 25! 25C4 = 4!(21!)

  6. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 25 24 23 22 21! 25C4 = 4 3 2 1 21!

  7. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 25C4 = 12,650

  8. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 12,650 n(all teachers): 5! 5C4 = 4!(5 – 4)!

  9. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 12,650 n(all teachers): 5! 5C4 = 4!(1!)

  10. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 12,650 n(all teachers): 5 4! 5C4 = 4! 1

  11. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 12,650 n(all teachers): 5C4 = 5

  12. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 12,650 n(all teachers): 5 n(all teachers) P(all teachers) = n(all selections)

  13. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 12,650 n(all teachers): 5 5 P(all teachers) = 12,650

  14. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 12,650 n(all teachers): 5 1 P(all teachers) = 2,530

  15. A committee of four out of 20 parents and 5 teachers a) P(all teachers) n(all selections): 12,650 n(all teachers): 5 P(all teachers) = 0.0004

  16. n(2 teachers and 2 parents): 5! 20! 5C2 20C2 = 2!(3!) 2!(18!) A committee of four out of 20 parents and 5 teachers b) P(2 teachers and 2 parents)

  17. A committee of four out of 20 parents and 5 teachers b) P(2 teachers and 2 parents) n(2 teachers and 2 parents): 5 4 20 19 5C2 20C2 = 2 1 2 1

  18. A committee of four out of 20 parents and 5 teachers b) P(2 teachers and 2 parents) n(2 teachers and 2 parents): 20 380 5C2 20C2 = 2 2

  19. A committee of four out of 20 parents and 5 teachers b) P(2 teachers and 2 parents) n(2 teachers and 2 parents): 5C2 20C2 = 10 190

  20. A committee of four out of 20 parents and 5 teachers b) P(2 teachers and 2 parents) n(2 teachers and 2 parents): 5C2 20C2 = 1,900

  21. A committee of four out of 20 parents and 5 teachers b) P(2 teachers and 2 parents) n(2 teachers and 2 parents): 1,900 P(2 teachers and 2 parents) = n(2 teachers and 2 parents) n(all selections) n(all selections): 12,650

  22. A committee of four out of 20 parents and 5 teachers b) P(2 teachers and 2 parents) n(2 teachers and 2 parents): 1,900 n(all selections): 12,650 P(2 teachers and 2 parents) = 1,900 12,650

  23. A committee of four out of 20 parents and 5 teachers b) P(2 teachers and 2 parents) P(2 teachers and 2 parents) =0.15

  24. n(all parents): 20! 20C4 = 4!(16!) A committee of four out of 20 parents and 5 teachers c) P(all parents)

  25. A committee of four out of 20 parents and 5 teachers c) P(all parents) n(all parents): 20 19 18 17 20C4 = 4 3 2 1

  26. A committee of four out of 20 parents and 5 teachers c) P(all parents) n(all parents): 116,280 20C4 = 24

  27. A committee of four out of 20 parents and 5 teachers c) P(all parents) n(all parents): 20C4 = 4,845

  28. A committee of four out of 20 parents and 5 teachers c) P(all parents) n(all parents): 4,845 n(all parents) P(all parents): n(all selections) n(all selections): 12,650

  29. A committee of four out of 20 parents and 5 teachers c) P(all parents) n(all parents): 4,845 n(all selections): 12,650 4,845 P(all parents): 12,650

  30. A committee of four out of 20 parents and 5 teachers c) P(all parents) P(all parents): 0.383

  31. n(1 teacher and 3 parents): 5! 20! 5C1 20C3 = 1!(4!) 3!(17!) A committee of four out of 20 parents and 5 teachers d) P(1 teacher and 3 parents)

  32. A committee of four out of 20 parents and 5 teachers d) P(1 teacher and 3 parents) n(1 teacher and 3 parents): 5 20 19 18 5C1 20C3 = 1 3 2 1

  33. A committee of four out of 20 parents and 5 teachers d) P(1 teacher and 3 parents) n(1 teacher and 3 parents): 5 6,840 5C1 20C3 = 1 6

  34. A committee of four out of 20 parents and 5 teachers d) P(1 teacher and 3 parents) n(1 teacher and 3 parents): 34,200 5C1 20C3 = 6

  35. A committee of four out of 20 parents and 5 teachers d) P(1 teacher and 3 parents) n(1 teacher and 3 parents): 5C1 20C3 = 5,700

  36. A committee of four out of 20 parents and 5 teachers d) P(1 teacher and 3 parents) n(1 teacher and 3 parents): 5,700 P(1 teacher and 3 parents) = n(1 teacher and 3 parents) n(all selections) n(all selections): 12,650

  37. A committee of four out of 20 parents and 5 teachers d) P(1 teacher and 3 parents) n(1 teacher and 3 parents): 5,700 n(all selections): 12,650 P(1 teacher and 3 parents) = 5,700 12,650

  38. A committee of four out of 20 parents and 5 teachers d) P(1 teacher and 3 parents) P(1 teacher and 3 parents) =0.450

  39. Chapter 11 Section 11.8 Exercise #3

  40. A city council consists of 10 members. Four are Republicans, three are Democrats, and three are Independents. If a committee of three is to be selected, find the probability of selecting All Republicans All Democrats

  41. (c) One of each party Two Democrats and one Independent One Independent and two Republicans

  42. A committee of 3 out of 10 members: 4 Republicans (R), 3 Democrats (D), 3 Independents (I) a) P(all R) n(all selections): 10! 10C3 = 3!(10 – 3)!

  43. A committee of 3 out of 10 members: 4 Republicans (R), 3 Democrats (D), 3 Independents (I) a) P(all R) n(all selections): 10! 10C3 = 3!(7!)

  44. A committee of 3 out of 10 members: 4 Republicans (R), 3 Democrats (D), 3 Independents (I) a) P(all R) n(all selections): 10 9 8 7! 10C3 = 3 2 1 7!

  45. A committee of 3 out of 10 members: 4 Republicans (R), 3 Democrats (D), 3 Independents (I) a) P(all R) n(all selections): 720 10C3 = 6

  46. A committee of 3 out of 10 members: 4 Republicans (R), 3 Democrats (D), 3 Independents (I) a) P(all R) n(all selections): 10C3 = 120

  47. A committee of 3 out of 10 members: 4 Republicans (R), 3 Democrats (D), 3 Independents (I) a) P(all R) n(all selections): 120 n(all R): 4! 4C3 = 3!(4 – 3)!

  48. A committee of 3 out of 10 members: 4 Republicans (R), 3 Democrats (D), 3 Independents (I) a) P(all R) n(all selections): 120 n(all R): 4! 4C3 = 3!(1!)

  49. A committee of 3 out of 10 members: 4 Republicans (R), 3 Democrats (D), 3 Independents (I) a) P(all R) n(all selections): 120 n(all R): 4 3! 4C3 = 3! 1

  50. A committee of 3 out of 10 members: 4 Republicans (R), 3 Democrats (D), 3 Independents (I) a) P(all R) n(all selections): 120 n(all R): 4C3 = 4

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