to Probability & Stochastic Processes I HOMEWORK 2 Problem 1 Suppose that a college has 1000 professors. a) In how many ways can the Board of Trustees pick a President? The President should be one of the 1000 professors. b) In how many ways can the Board of Trustees pick a President and a Provost? c) The Board of Trustees want to pick a team of 5 faculty members for a search committee to find a new President for the college. In how many ways can they do that? Problem 2 We construct all the words we can by permuting the letters of the word `MISSISSIPPI' (does not matter if they are valid English words or not). Then we pick a word at random from that set. What is the chance of observing `MISSISSIPPI'? Problem 3 We toss a fair coin 10 times. What is the probability of observing at least one head? (Note: For a fair coin, the probability of observing heads in each tossing is the same as observing tails.) Problem 4 A university warehouse has received a shipment of 25 printers, of which 10 are laser printers and 15 are inkjet models. If 6 of these