5. Suppose there are 15 students in the class. One of the student is a first year student. One day I decide to choose some of the students to form a team to enter a software competition. Suppose there is no upper limit on the number of students in the team, but a team should have at least 2 members. Also first year students are not allowed to enter the competition. How many different ways are there to determine the members of such a team?

A course has 30 students and four possible letter grades A, B, C, D. What is the maximum number of students who are guaranteed to obtain the same grade

There are 28 students in a class who want to be members in the school 's physics, math and literature clubs having only 6,8 and 10 open seats respectively. Sadly, some of the students will not be able to join any club. In how many ways can the students become members of the different clubs to their full capacity?

Phoenix is a hub for a large airline. Suppose that on a particular day, 8,000 passengers arrived in Phoenix on this airline. Phoenix was the final destination for 1,600 of these passengers. The others were all connecting to flights to other cities. On this particular day, several inbound flights were late, and 410 connecting passengers missed their connecting flight and were delayed in Phoenix. Of the 410 who were delayed, 85 were delayed overnight and had to spend the night in Phoenix. Consider the chance experiment of choosing a passenger at random from these 8,000 passengers. Calculate the following probabilities. (Round your answers to three decimal places.) (a) Calculate the probability that the selected passenger had Phoenix as a final destination. (b) Calculate the probability that the selected passenger did not have Phoenix as a final destination. (c) Calculate the probability that the selected passenger was connecting and missed the connecting flight. (d) Calculate the…