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AMS 301 2nd tests

# AMS 301 2nd tests - AMS 301 SECOND TEST Test A Fall 2009 1...

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AMS 301 SECOND TEST Test A Fall, 2009 1. Find the coefficient of x^24 in (x^3+ x^4+ x^5+ x^6)^5. 2. Consider the problem of counting the ways to select 25 objects from 6 types with at least two objects of each type. a) Model this problem as an integer-solution-of-equation-problem.(BR> b) Model this problem as a certain coefficient of a generating function. c) Solve this problem. 3. Find the probability that 4-card hand (from a 52-card deck) has no pair each card of a different kind). 4. How many 6-digit decimal sequences are there with exactly r 3's. 5. How many arrangements of MATHEMATICAL are there in which ME appear together but ME is not immediately followed by an A (no MEA)? 6. How many arrangements of letters in ORIGINATING have ALL of the following pr operties: (i) at least two letters between each I, (ii) begins or ends (not both) with an I, and (iii) the consonants are in alphabetical order. 7. You have 6 friends. How many ways are there to invite a different subset of two of these friends over for dinner on 5 successive nights.

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AMS 301 2nd tests - AMS 301 SECOND TEST Test A Fall 2009 1...

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