COT 3100 Assignment 10

1. A programming club has 6 members consisting of 4 female and 2 male students. The club rules do not allow any member to serve in more than one leadership position.

a. In how many ways the club leadership consisting of a president, a vice president and a treasurer can be selected? (Justify your answer)

b. If the rules do not allow any member to serve in more than one position, in how many different ways the club leadership can be chosen if we require that the president be a female and treasurer be a male (Justify your answers).

2. There are 3,000 students majoring in computer Science. By applying generalized pigeonhole principle, determine the minimum number of Computer Science students who have the same initials (first letter of the first name followed by the first letter of the last name). Clearly state how you applied the generalized pigeonhole principle to arrive at your solution.

3. Students in a class take two exams: exam1 and Exam2. The exams are graded a scale of 0-2. What is the minimum number of students that guarantee the at least 2 students will receive the same in both exams. Justify your answer.