Step 5: Select the check digit: 9 choice (exclude the correct check digit). Total number of choices:2×107×103×9 = 18×1010 = 180billion possible card numbers 43. a.Steps 1–3: Choose three bases (4 choices each):43 = 64choices b.Steps 1–: Choosebases (4 choices each):4choices c.From part (b) with= 2.1×1010,we obtain a total of4= 42.1×10 10 possible DNA chains. 44. a.Steps 1–4: Choose four bases (6 choices each):64 = 1,296choices b.Steps 1–: Choosebases (6 choices each):6choices c.From part (b) with= 2.1×1010,we obtain a total of6= 62.1×10 10 possible expanded DNA chains. 45. a.Steps 1–6: Select 6 hexadecimal digits (16 choices per digit):166 = 16,777,216 possible colors b.Step 1: Choose the 1st repeating pair of digits: 16 choices. Step 2: Choose the 2nd repeating pair of digits: 16 choices. Step 3: Choose the 3rd repeating pair of digits: 16 choices. Total number of colors:163 = 4,096 c.Step 1: Choose the digit:16 choices. Step 2: Choose the digit:16 choices. Total number of grayscale shades:162 = 256 d.Step 1: Choose the position for the sequence:3 choices. Step 2: Choose the values ofand:16^{2} choices.

SSoolluuttiioonnssSSeeccttiioonn66..33 Total number of choices:3×162 choices. However, the above decision algorithm leads to the sequence 000000 in three ways. The number of pure colors is therefore3×162 −2 = 766. 46.Steps 1–2: Select 2 digits in the range 2–9: 8 choices per step:82 choices. Steps 3–7: Select 5 digits in the range 0–9; 10 choices per step:105 choices. Total:82×105 = 6,400,000telephone numbers 47.Step 1: Choose a male actor to play Escalus: 10 choices. Step 2: Choose a male actor to play Paris: 9 choices. ... Step 6: Choose a male actor to play Tybalt: 5 choices. Step 7: Choose a male actor to play Friar Lawrence: 4 choices. Step 8: Choose a female actor to play Lady Montague: 8 choices. Step 9: Choose a female actor to play Lady Capulet: 7 choices. Step 10: Choose a female actor to play Juliet: 6 choices. Step 11: Choose a female actor to play Juliet's Nurse: 5 choices. Total number of casts:(10×9×8×7×6×5×4)×(8×7×6×5) = 1,016,064,000 48.Step 1: Choose a female actor to play Prince Siegfried: 4 choices Step 2: Choose a female actor to play Rotbart: 3 choices. Step 3: Choose a male actor to play Friar Siegfried's Mother: 12 choices. Step 4: Choose a male actor to play Princess Odette: 11 choices. Step 5: Choose a male actor to play Odile: 10 choices. Step 6: Choose a female actor to play Cygnet #1: 9 choices. Step 7: Choose a female actor to play Cygnet #2: 8 choices. Step 8: Choose a female actor to play Cygnet #3: 7 choices. Total number of casts:(4×3)×(12×11×10×9×8×7) = 7,983,360 49. a.Steps 1–3: Choose 3 letters:263 choices. Steps 4–6: Choose 3 digits:103 choices. Total number of license plates:263×103 = 17,576,000 b.Steps 1–2 Choose 2 letters:262 choices. Step 3: Choose a letter other than I, O, or Q: 23 choices. Steps 4–6: Choose 3 digits:103 choices. Total number of license plates:262×23×103 = 15,548,000 c.A decision algorithm for the number of reserved plates: Step 1: Choose VET, MDZ, or DPZ: 3 choices.

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