ENGRD2700F11HW2(3)

# ENGRD2700F11HW2(3) - ENGRD 2700 F11 Homework 2 1 There are...

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ENGRD 2700 F11 Homework 2 1. There are 48 Master of Engineering students to assign to projects this year. Suppose project teams must consist of exactly 4 people. How many different ways are there to construct a single project team? What if the team must consist of 2 men and 2 women, and there are 28 men and 20 women students? 2. (Based on a real application). A certain oil refinery keeps intermediate products in 8 tanks (tanks are different for this question). There are 20 pumps of varying capacity that can be assigned to pump the intermediate product from the 8 tanks into a final-product tank. How many ways can you assign the 20 pumps to the 8 tanks (so that each tank gets at least one pump)? To answer this question, we can proceed as follows: Let d ( k, n ) be the number of ways to assign k pumps to n tanks in such a way that each tank gets at least one pump. (a) Explain why d ( k, 1) = 1 for all k > 0. Also explain why d ( k, n ) = 0 for n > k . (b) Show that for k > 1 and n 1, d ( k, n ) = nd ( k - 1 , n ) + nd ( k - 1 , n - 1) . (c) Hence or otherwise, answer the question. Feel free to use some software, e.g., Excel. (d) We want to determine the assignment of pumps to tanks that minimizes the time required to pump the intermediate products. Assuming we have a computer that can analyze one million assignments each second, how long would it take the computer to analyze all possible assignments?

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