# hw09 - CS 70 Spring 2005 Discrete Mathematics for CS...

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CS 70 Discrete Mathematics for CS Spring 2005 Clancy/Wagner HW 9 Due Thursday, April 7 Coverage: This assignment involves topics from the lectures of March 15, 17, 29, and 31, and from Rosen sections 4.4 and 5.1. The assignment is shorter than usual because of the April 5 exam. Administrative reminders: We will accept only unformatted text files or PDF files for homework sub- mission. Include your name, login name, section number, and partner list in your submission. Give the command submit hw9 to submit your solution to this assignment. Homework exercises: 1. (50 pts.) Binomial coefficients This question will teach you about binomial coefficients. As was explained in class, suppose we want to count how many different ways there are to choose a subset of m objects from a set of n different objects. Assume that repetition is not allowed, and the order in which you choose the m objects is ignored. The answer, of course, is n ! m ! ( n - m ) ! . This is such an important value that we define the notation ( n m ) as short-hand for n ! m ! ( n - m ) ! . This is called the binomial coefficient “ n choose m ”, and you will sometimes see it written C ( n , m ) in other texts. As a matter of convention, if

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