MATH 180 Midterm: Math 180 Exam 2
Document Summary
This test is closed book and closed notes. For full credit show all of your work and (brie y) explain your approach (legibly! We need to count two things, the number of outcomes with the restriction that there is at least one orange and at least one apple per person, and the number of possible outcomes. To count the rst thing we need to distribute the 8 oranges. To make sure that everyone gets at least one orange we rst give one orange to each person. This leaves 5 oranges (balls) to distribute among 3 people (bins) which can be done in (cid:0)5+3 1. Since each person must have at least one then we can distribute apples in one of the following ways: (1, 2, 2), (2, 1, 2), (2, 2, 1), (1, 1, 3), (1, 3, 1) and (3, 1, 1). In the rst three cases this can be done in 5!
