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04spex1sam

# 04spex1sam - Math 431 Sample First Evening Exam Room B239...

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Math 431 Sample First Evening Exam Room B239, 6:15 - 7:15pm, February 23, 2004 M´arton Bal´azs 1. (45 points) “ Aoccdrnig to a rscheearch at an Elingsh uinervtisy, it deosn’t mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht frist and lsat ltteer is at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae we do not raed ervey lteter by itslef but the wrod as a wlohe. Based on this research, let’s assume that an English word is uniquely determined by its first and last letter, and the unordered set of its other letters. Put it in another way, given an English word, changing the order of the inner letters (and so leaving the first and last letter fixed) cannot lead to a different English word. Give then an upper bound on the number of five-letter English words, and compare it to the number of all possible sequences of length five, composed of any of the 26 letters of the alphabet.

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04spex1sam - Math 431 Sample First Evening Exam Room B239...

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