This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 Pascals identity involving the binomial coefficients. Binomial Theorem: ( x + y ) n = n summationdisplay k =0 parenleftbigg n k parenrightbigg x k y n k . Pascals 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?...
View
Full
Document
 Spring '11
 HuangJing
 Math

Click to edit the document details