An advisory committee is being formed for a new project at a company. The committee has 6 identical positions to be filled. The committee is to consist of 2 people chosen from the Research and Development Department, which has a total of 12 employees, and 4 people from the Marketing Department, which has a total of 20 employees. How many total possible advisory committees could be formed from these choices?

The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 72 ​students, requires 7 ​chaperones, and costs $1300 to rent. Each van can transport 8 ​students, requires 1​ chaperone, and costs ​$90 to rent. Since there are 720 students in the senior class that may be eligible to go on the​ trip, the officers must plan to accommodate at least 720 students. Since only 84 parents have volunteered to serve as​ chaperones, the officers must plan to use at most 84 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation​ costs? What are the minimal transportation​ costs?

In a restaurant servers are constantly bringing out beverages to their tables. If a restaurant had a dining hall with only 4-seated tables, how many combinations of soft drinks could the servers bring out if they only had {Coke, Sprite, Fanta}?

There are 11 students in a kindergarten class. If each kindergartner can have only one task, in how many ways can the teacher assign out the following tasks: line leader, wipe down the tables, pass out papers, water the plants, erase the board?

You manage a team of 4 employees. The entire team is responsible for completing 4 projects on time. The time to complete the task is 4 weeks, and this is the time needed and is based on a 56-hour work week for each team member. Each team member will work 7 days a week, since this is a priority project and, must be completed on time. The names of the 4 team members are A, B, C, and D. Based on historical data, at least 1 of the 4 team members calls in sick at least (and only) 1 time per week. Based on this information, what is the probability that the project will be completed on time? If the probability of the project not being completed on time is > 0, what will you do to ensure that the project will be completed on time? What AI systems would you put in place to ensure that you can complete current and future projects? You are to select a strategy that is most feasible and you must justify your answer and provide an analysis.

Suppose you have a choice of ten TV sets that can be matched with any of six DVR players and eight DVD players. How many different TV/DVR/DVD systems can you assemble?

You have 4 indistinguishable gold coins and 4 indistinguishable silver coins. Each coin has a side that is heads and a side that is tails. You want to stack the eight coins on a table into a single stack so that no two adjacent coins are face to face. Find the number of possible distinguishable stacks of the 8 coins.

Jack, Anny and Bella were elected as Executive Officers in their organization. They will be appointed to the posts of Chairman, Treasurer, and Secretary. Since Anis has already been the Secretary for four terms, he is ineligible for the Secretary post. How many possible formations of the posts are there?

In her last semester at SPC, Polly Hedron needs to take Statistics, Composition 2, and Ethics.  Because Polly is registering early, she has 13 choices for her section of Statistics, 15 choices for her section of Composition, and 20 choices for her section of Ethics.  From how many possible schedules can Polly choose?

Carmine is creating a schedule for five key presenters who will be speaking to students on career day. They have hired a doctor, an engineer, a pilot, a lawyer, and an accountant. What is the number of possible arrangements if the engineer must speak after the lawyer?