# Homework 2 _SOLUTION

1. Count the number of outcomes in the following:(a) There are 12 varieties of apples, and any of them can be either organic or conventional, and any of those can be local or not local. How many diﬀerent types of apples are there? (b) There are 5 episodes in a hit TV series. How many diﬀerent DVDs can there be which contain two of the episodes, when the order of the episodes on the DVD doesn’t matter? (c) There are 10 chairs in a classroom. How many ways are there for 10 students to be seated in them? (d) There are 10 chairs in a classroom. How many ways are there for 8 students to be seated in them? (e) There are 10 chairs in a classroom. Five couples are enrolled in the class. How many ways are there for them to be seated if each couple must be seated next to each other? 2. Walpole 2.47. Copied here: How many ways are there to select three candidates from 8 equally qualiﬁed recent graduates for openings in an accounting ﬁrm? Assume order doesn’t matter. 3. Walpole 2.48. Copied here: How many ways are there that no two students have the same birth date in a class of 60? Neal’s note: assume that year is not included in “birth date”, and you can approximate by not accounting for leap years. 4. (Adapted from Tolga Tasdizen): We have a bag with 5 red marbles and 9 blue marbles. You draw three marbles out of the bag without replacement. (a) What is the probability that you got a red, blue, and red marble in that order? Hint: use the multiplication rule to get the size of the sample space (and size of the event set) as if the marbles were distinguishable. (b) What is the probability of not getting any blue marbles? (c) What is the probability you got two red and one blue marble, in any order? Hint: add the numbers of each ordering of getting two reds and one blue marble.