Probability and Counting Principles: Get Stronger Answer Key

Counting Principles

  1. [latex]4 + 2 = 6[/latex]
  2. [latex]5 + 4 + 7 = 16[/latex]
  3. [latex]2 \times 6 = 12[/latex]
  4. [latex]10^3 = 1000[/latex]
  5. [latex]P(5,2) = 20[/latex]
  6. [latex]P(3,3) = 6[/latex]
  7. [latex]P(11,5) = 55,440[/latex]
  8. [latex]C(12,4) = 495[/latex]
  9. [latex]C(7,6) = 7[/latex]
  10. [latex]2^{10} = 1024[/latex]
  11. [latex]2^{12} = 4096[/latex]
  12. [latex]2^9 = 512[/latex]
  13. [latex]\frac{8!}{3!} = 6720[/latex]
  14. [latex]\frac{12!}{3!2!3!4!}[/latex]
  15. [latex]6 - 3 + 8 - 3 = 8[/latex]
  16. [latex]4 \times 2 \times 5 = 40[/latex]
  17. [latex]4 \times 12 \times 3 = 144[/latex]
  18. [latex]P(15,9) = 1,816,214,400[/latex]
  19. [latex]C(10,3) \times C(6,5) \times C(5,2) = 7,200[/latex]
  20. [latex]2^{11} = 2048[/latex]
  21. [latex]\frac{20!}{6!6!8!} = 116,396,280[/latex]

Binomial Theorem

  1. [latex]15[/latex]
  2. [latex]35[/latex]
  3. [latex]10[/latex]
  4. [latex]12,376[/latex]
  5. [latex]64a^3 - 48a^2b + 12ab^2 - b^3[/latex]
  6. [latex]27a^3 + 54a^2b + 36ab^2 + 8b^3[/latex]
  7. [latex]1024x^5 + 2560x^4y + 2560x^3y^2 + 128x^2y^3 + 320xy^4 + 32y^5[/latex]
  8. [latex]1024x^5 - 3840x^4y + 5760x^3y^2 - 4320x^2y^3 + 1620xy^4 - 243y^5[/latex]
  9. [latex]\frac{1}{x} + \frac{24}{x^5y} + \frac{32}{x^8y^2} + \frac{16}{x^{11}y^3} + \frac{3}{y^4}[/latex]
  10. [latex]a^{17} + 17a^{16}b + 136a^{15}b^2[/latex]
  11. [latex]a^{15} - 30a^{14}b + 420a^{13}b^2[/latex]
  12. [latex]3,486,784,401a^{20} + 23,245,229,340a^{19}b + 73,609,892,910a^{18}b^2[/latex]
  13. [latex]x^{24} - 8x^{21}\sqrt{y} + 28x^{18}y[/latex]
  14. [latex]-720x^2y^3[/latex]
  15. [latex]220,812,466,875,000y^7[/latex]
  16. [latex]35x^3y^4[/latex]
  17. [latex]1,082,565a^3b^{10}[/latex]
  18. [latex]\frac{1152y^2}{x^7}[/latex]

Introduction to Probability

  1. [latex]\frac{1}{2}[/latex]
  2. [latex]\frac{5}{8}[/latex]
  3. [latex]\frac{1}{2}[/latex]
  4. [latex]\frac{3}{8}[/latex]
  5. [latex]\frac{1}{4}[/latex]
  6. [latex]\frac{3}{4}[/latex]
  7. [latex]\frac{3}{8}[/latex]
  8. [latex]\frac{1}{8}[/latex]
  9. [latex]\frac{15}{16}[/latex]
  10. [latex]\frac{5}{8}[/latex]
  11. [latex]\frac{1}{13}[/latex]
  12. [latex]\frac{1}{26}[/latex]
  13. [latex]\frac{12}{13}[/latex]
  14. 1 2 3 4 5 6
    1 [latex](1,1)\\2[/latex] [latex](1,2)\\3[/latex] [latex](1,3)\\4[/latex] [latex](1,4)\\5[/latex] [latex](1,5)\\6[/latex] [latex](1,6)\\7[/latex]
    2 [latex](2,1)\\3[/latex] [latex](2,2)\\4[/latex] [latex](2,3)\\5[/latex] [latex](2,4)\\6[/latex] [latex](2,5)\\7[/latex] [latex](2,6)\\8[/latex]
    3 [latex](3,1)\\4[/latex] [latex](3,2)\\5[/latex] [latex](3,3)\\6[/latex] [latex](3,4)\\7[/latex] [latex](3,5)\\8[/latex] [latex](3,6)\\9[/latex]
    4 [latex](4,1)\\5[/latex] [latex](4,2)\\6[/latex] [latex](4,3)\\7[/latex] [latex](4,4)\\8[/latex] [latex](4,5)\\9[/latex] [latex](4,6)\\10[/latex]
    5 [latex](5,1)\\6[/latex] [latex](5,2)\\7[/latex] [latex](5,3)\\8[/latex] [latex](5,4)\\9[/latex] [latex](5,5)\\10[/latex] [latex](5,6)\\11[/latex]
    6 [latex](6,1)\\7[/latex] [latex](6,2)\\8[/latex] [latex](6,3)\\9[/latex] [latex](6,4)\\10[/latex] [latex](6,5)\\11[/latex] [latex](6,6)\\12[/latex]
  1. [latex]\frac{5}{12}[/latex]
  2. [latex]0[/latex]
  3. [latex]\frac{4}{9}[/latex]
  4. [latex]\frac{1}{4}[/latex]
  5. [latex]\frac{5}{8}[/latex]
  6. [latex]\frac{3}{13}[/latex]
  7. [latex]\frac{C(12,5)}{C(48,5)} = \frac{1}{2162}[/latex]
  8. [latex]\frac{C(12,3)C(36,2)}{C(48,5)} = \frac{175}{2162}[/latex]
  9. [latex]\frac{C(55800000,1)C(275200000,4)}{C(331000000,5)} = 40.28 \%[/latex]
  10. [latex]\frac{C(55800000,4)C(275200000,1)}{C(331000000,5)} = .336 \%[/latex]