301 old 3rd tests - Third Test of Tucker's AMS 301 course...

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Third Test of Tucker's AMS 301 course Fall 2009 Third Test for Tucker's AMS 301 course 1. Find the rook polynomial and give an expression for the number of matchings of 5 men (Rows) and 5 women (Columns) given the follow 8 conflicting pairs: (M1,W4),(M2,W2),(M3,W1), (M3,W3),(M3,W5),(M4,W3),(M5,W2),(M5,W4). 2. How many ways are there to arrange the letters in the word STATISTICS so that the three S's do not appear consecutively and the three T's are not consecutive and the two I's are not consecutive? 3. Find a rec. rel for an,k, the number of ways to select n donuts from k diff. types of donuts with 3 or 5 or 8 donuts chosen of each type. 4. a) Find a recurrence relation for an, the number of sequences of 2's, 3's and 5's whose sume is n. b) Repeat part a) with the requirement that noo 4 can be followed by a 2. 5. There are 8 Broadway musicals and they offer a special three-night package ( Friday, Saturday, Sunday nights) where one can order a single ticket that is good for three different musicals on successive nights (a SEQUENCE of three musicals). A travel agent is going to order a collection
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