N = {Alan, Bill, Cathy, David, Evelyn}.

Assuming that all members are eligible, but no one can hold more than one office, list and count the different ways the club could elect each group of officers. (Cathy and Evelyn are women, and the others are men.)

5. a president and a treasurer

6. a president and a treasurer if the president must be a woman

7. a president and a treasurer if the two officers must be the same sex

8. a president, a secretary, and a treasurer, if the president and treasurer must be women

9. a president, a secretary, and a treasurer, if the president must be a man and the other two must be women

10. a president, a secretary, and a treasurer, if all three officers must be men.

38. Construct a product table showing all possible two-digit numbers using digits from the set

{2, 3, 5, 7}.

Of the sixteen numbers in the product table for Exercise 38, list the ones that belong to each category.

39. numbers with repeating digits

40. even numbers

41. prime numbers

42. multiples of 3

43. Construct a tree diagram showing all possible results when three fair coins are tossed. Then list the ways of getting each result.

(a) at least two heads

(b) more than two heads

(c) no more than two heads

(d) fewer than two heads

44. Extend the tree diagram of Exercise 43 for four fair coins. Then list the ways of getting each result.

(a) more than three tails

(b) fewer than three tails

(c) at least three tails

(d) no more than three tails