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COT3100C01, 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 unsimplified form, e.g., 5! / 3!, 2
9
* (2
4
+ 6 * 2
3
), etc.
1.
(12 pts.) Count the number of 7digit 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
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This document was uploaded on 07/14/2011.
 Spring '09

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