In Exercise 1.1.6 the number of ways that all pairwise comparisons could be made among 10 people was determined by counting all of the events, and the answer was
9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45.
a. Use combinations to verify that answer.
b. Why do both procedures produce the same answer?
Exercise 1.1.6
The grading of laboratory reports is tedious, so a laboratory instructor decides that he will grade only a randomly chosen 2 of the 5 reports that each student has submitted.
If both are acceptable, the student will be given an A as his laboratory grade; if 1 is acceptable, he will receive a B; a C will be given if neither is acceptable.
a. How likely is a student to receive an A when he has submitted 5 acceptable reports? 4? 3? 2? 1? 0?
b. How likely is a student to receive a C when he has submitted 5 acceptable reports? 4? 3? 2? 1? 0?