1 A sixperson committee composed of Brendan Melissa Jason Pa

1. A six-person committee composed of Brendan, Melissa, Jason, Paula, Eric, and Jon is to select a chairperson, secretary, and treasurer. How many selections are there in which at least one office is held by Brendan or Jon? Note: Assume that each person can hold at most one office.

2. In how many ways can we select a president, vice-president, and treasurer from a group of 11 people? Note: Assume here that the same person can hold more than one office.

3. Suppose you go into a restaurant offering sandwiches that allows you to choose from 9 vegetables and 12 sauces to add. If you decide to include 4 different vegetables and 2 different sauces, how many ways are there to make this choice?

4. Suppose that you have 4 red Jolly Ranchers, 3 yellow Jolly Ranchers, 3 green Jolly Ranchers, and you are hanging out with 10 friends. Assuming that the Jolly Ranchers of the same color are indistinguishable, how many ways can you give one Jolly Rancher to each of your friends? Hint: Mississippi.

5. Expand (5c 4d)^4 using the Binomial Theorem.

6.  You are tasked with reforming the (Gregorian) calendar to make it easier to use. Instead of the twelve months having numbers of days that vary so much (from 28 to 31), you are going to even things up more (add days to February, etc.). Show that no matter what you do with twelve months, there must be some month with at least 31 days.

Solution