Which of the following events are mutually exclusive?

A company has 15 employees. Four are managers, six are engineers, and five are interns. In how many ways can the company select a CEO, a CFO, and a COO, given that only a manager can be the CEO, and the other two positions can be filled by any employee, with no one holding more than one position

Consider the following circuits of 4 identical relays. The probability that any relay works is 0.7 and the failures of the relays are independent. What is the probability that, when current is applied, it flows from point 1 to 2?    

An article in The Journal of Data Science  provided the following table of well failures for different geological formation groups in Baltimore County.    Geological Formation Group Wells Failed Wells Total Gneiss 170 1685 Granite 2 28 Loch raven schist 443 3733 Mafic 14 363 Marble 29 309 Prettyboy schist 60 1403 Other schists 46 933 Serpentine 3 39   Let A denote the event that the geological formation has more than 1000 wells, and let B denote the event that a well failed. Determine the number of wells in each of the following events.   Find the following, P(A Bc)  

An bag contains 15 marbles of which 10 are red and 5 are white. 5 marbles are selected from the bag. How many samples (of size 5) have at most 2 red marbles?

Suppose that a 12% discount is independently applied to online orders for electronics with a probability of 0.2. What is the probability that the first discount is applied to the fourth order?

Find the general antiderivative. Assume

Suppose that and are integrable and that 

The base pair on top is most likely:

You are examining chromatin structure in strawberries.  After isolating the chromatin and performing a short digestion with micrococcal nuclease you find the following banding pattern on a gel:  650bp, 1300 bp, 1950 bp, 2600 bp.  Approximately how long is the linker DNA in these cells?