Six different groups of children would like to visit the zoo and feed different animals. (Assume each group will visit the zoo on only one day.) Group 1 would like to feed the bears, dolphins, and gorillas. Group 2 would like to feed the bears, elephants, and hippos. Group 3 would like to feed the dolphins and elephants. Group 4 would like to feed the dolphins, zebras, and hippos. Group 5 would like to feed the bears and hippos. Group 6 would like to feed the gorillas, hippos, and zebras. Use graph coloring to find the minimum number of days that are required so that all groups can feed the animals they would like to feed but no animals will be fed twice on the same day.

A co-rec team to play in an intramural tournament of indoor soccer should consist of three men and three women. There are five men and ten women to join that team. Within the fifteen people there is a husband and wife. In how many ways can that team be selected if it must contain either the wife or the husband but not both?

Suppose you visit a small, local panadería and decide to pick up some pasteries. The panadería has a selection of 8 different cupcakes, 14 different donuts ,7 different muffins ,2 types of donut holes , and 11 different types of pan dulce. You  pick one of each. How many different orders are possible.

Mr. Smith decides to organize a potluck party with neighbors on a weekend. John Smith and his wife Mary Smith and his daughter Judy Smith will prepare three different salad dishes. John's right side neighbor Jenny Jones and Bob Jones will prepare two desserts. John's left side neighbor Linda will prepare one meat dish. John's cross street neighbor Sue will prepare soup. John wants to figure out how many different ways for him to taste all dishes in order (assuming he will taste all salads, meat, desserts and soup). (Note : For example, "Salad, Soup, Salad, Meat, Dessert, Salad, Dessert" is one of the possible order he can try.

2.) The BOS-14 is the new model of cars manufactured by NUC Motors. This model can be achieved in 2 body styles, 4 interior options and 7 different colors. The model can be achieved in automatic transmission as a manual. ER Auto wants to have a model of each of the options available to sell. How many BOS-14 models should you order?

For dinner there are two choices of fish (salmon and haddock), three choices of rice (brown, jasmine, or pilaf), and four types of vegetables.  How many different meals can be made with one fish, one rice, and one vegetable?

Tony Soprano orders three of his henchmen to go and get cannolis. Silvo returns with bag A, which has two white vanilla cannolis. Paulie returns with bag B, which has two black chocolate cannolis. Christopher comes back with bag C, which has one white vanilla and one black chocolate cannoli. Tony reaches into one bag at random and takes a big bite of a white vanilla cannoli. Tony says, “Hey this is pretty good! Hey, Christopher, you just graduated from UWT. Did that Goda guy teach you anything? What are the odds the other cannoli in the bag I grabbed is a white vanilla cannoli?” Well Christopher, what do you say?

A shoe company wants to test an updated model of a running shoe on its wear after one month of running. Which of the following describes a matched pairs design? They recruit 50 people who run on a regular basis to participate in their study. They will have the runners wear the shoes when they run for two months. After two O The subjects are numbered 1-50, and these numbers are put into a random number generator. The first 25 random numbers, ignoring repeats, represent the subjects assigned to the new model group. The remaining 25 subjects will wear the original model. months, the wear on the shoes will be determined using the depth of the tread and flexibility of the toe box. The wear between the new model and the original model will then be compared. The subjects' names are written on equal-sized slips of paper and placed into a hat. A researcher then reaches in and pulls out 25 slips of paper. These subjects are assigned to the new model group. The remaining 25 subjects will be…

At your local carnival, there is a game where 40 rubber duckies are floating in a kiddie tub, and they each have their bottoms painted one of three colors. 55 are painted pink, 16 are painted blue, and 19 are painted purple. If the player selects a duck with a pink bottom, they receive three pieces of candy. If they select blue, they receive two pieces of candy. And if they select purple, they receive one piece of candy. If the game is played 42 times, what are the minimum and maximum amounts of candy that could be handed out?

Assume Amy is making a sandwich for lunch and needs to select her sandwich fixings. She will select two meats out of 5 options, 1 cheese out of 3 options, and exactly 3 or exactly 5 vegetables out of the 7 options. She will also decide whether to add mayo or not. How many ways can she make her sandwich.