Lecture 6 Homework: Counting Techniques 7. A class contains 10 students with 6 men and 4 women. Find the number of (a) (2.5 pt.) Select a 4-member committee from the students. ways to: (b) (2.5 pt.) Select a 4-member committee with 2 men and 2 women. (c) (2.5 pt.) Elect a president, vice president, and treasurer. (5 pt.) Find the number of committees of 5 with a given chairperson that can be selected from 12 people. 8. 9. Find the minimum number n of integers to be selected from S (a) (2.5 pt.) The sum of two of the n integers is even. (1,2,...9) so that: (b) (2.5 pt.) The difference of two of the n integers is 5. 10. (5 pt.) 11 numbers are chosen from the integers from 1 to 20. Prove that 2 of the chosen integers are consecutive