Diana​ Baniak, searching for an Ecology​ class, knows that it must be in one of seven classrooms. Since the professor does not allow people to enter after the class has​ begun, and there is very little time​ left, she decides to try just three of the rooms at random. How many of the possible different selections of three rooms will succeed in locating the​ class?

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…

Suppose you want to select two types of snacks and one drink in a coffee shop. There are 5 choices of snacks and 10 types of drinks to choose from. If you don't want to pick the same snack twice, how many different combinations of 2 snacks and 1 drink could you have? Note, we consider the order of choosing snacks does not matter.

In a survey, 200 restaurants were asked to select which of the following options were on their menu: tacos, burgers. 98 of the restaurants serve tacos and 74 of the restaurants serve burgers. 37 of the restaurants serve neither of these options.  How many of the restaurants serve both tacos and burgers? Show your work.