222m1 - MATH 222 [A01] Fall 2011 First Midterm Test...

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Unformatted text preview: MATH 222 [A01] Fall 2011 First Midterm Test Instructor: Dr. Jing Huang October 12, 2011 3:30 - 4:20pm Instructions: This question paper has six pages plus cover. For each question, write out your solution/answer carefully in the space provided. Use the back of pages if necessary. Marks will be deducted for incomplete or poorly presented solutions/answers. The Sharp EL-510R calculator is the only calculator permitted. No other aids (such as books, notes, formula lists, or scratch paper) are allowed. Questions Value Marks 1 4 2 6 3 5 4 6 5 5 6 4 Total 30 Name: Id: .../1 1 1. (a) State the binomial theorem and the Pascals identity involving the binomial coefficients. [2] (b) Determine the coefficient of x 2 y 5 in the expansion of ( x + 2 y + 1) 10 . [2] .../2 2 2. How many strings of length 14 are there, using symbols from { U, V, I, C } , such that (a) each string contains exactly two U s, three V s, four I s, and five C s? [2] (b) each string contains exactly two U s which are...
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222m1 - MATH 222 [A01] Fall 2011 First Midterm Test...

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