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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 EL510R 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: Answer Key Id: V20111012 .../1 1 1. (a) State the binomial theorem and the Pascal’s identity involving the binomial coefficients. Binomial Theorem: ( x + y ) n = n summationdisplay k =0 parenleftbigg n k parenrightbigg x k y n k . Pascal’s Identity: parenleftbigg n k parenrightbigg = parenleftbigg n − 1 k parenrightbigg + parenleftbigg n − 1 k − 1 parenrightbigg . (b) Determine the coefficient of x 2 y 5 in the expansion of ( x + 2 y + 1) 10 . The coefficient is parenleftbigg 10 2 , 5 , 3 parenrightbigg 2 5 = 10! 2!5!3! 2 5 . .../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?’s?...
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This note was uploaded on 01/15/2012 for the course MATH 222 taught by Professor Huangjing during the Spring '11 term at University of Victoria.
 Spring '11
 HuangJing
 Math

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