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hw3fa02 - COT3100C-01 Fall 2002 S Lang Assignment#3(40 pts...

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COT3100C-01, Fall 2002 Assigned: 10/03/2002 S. Lang Assignment #3 (40 pts.) Due: 10/15 in class by 8:45 am Instructions: Write your answer neatly and concisely. Show all your work and explain each of the steps and how the formulas are applied. Illegible scribbles or unclear logic will result in minimum credit . Answers without explanation receive zero credit. You may leave your answers in an un-simplified form, e.g., 5! / 3!, 2 9 * (2 4 + 6 * 2 3 ), etc. 1. (12 pts.) Count the number of 7-digit integers under each of the following restrictions: (a) All digits are distinct. (Thus, integers such as 1234567 and 3456980 are counted, but integers such as 2345 and 2233445 are not counted.) (b) The digits may be repeated (such as 2233456) but the integer must be divisible by 5. (Hint: what would be the last, rightmost digit for an integer to be divisible by 5?) (c) The digits may be repeated but digit 3 must be used (as part of the integer) at least twice. (Hint: consider the cases: digit 3 used twice, three times, etc., until 7 times, then count each case or group separately. Alternatively, consider the complementary question, i.e, if digit 3 is not used
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