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# s9 - Math 55 Worksheet Instructions Today you’ll be...

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Unformatted text preview: Math 55 Worksheet Instructions: Today you’ll be working with TWO different groups. In group 1 you’ll all be working on the same problem. Then we’ll switch into larger groups with one ambassador from each problem. The ambassador will lead the group in writing solutions on the board! In group one, first solve your own problem. Once you’re done, let me know, and then try and solve the Tough Problems at the bottom. Counting and Pigeon Hole 1. (a) How many different functions are there from a set with n elements to a set with m elements? (b) How many different injective functions are there from a set with n elements to a set with m elements? You may assume n ≤ m Solutions are in Section 6.1 2. How many strings of 5 decimal digits (a) contain at least one 4? Solution: Hint! anytime you see something that is trying to count strings with AT LEAST something. It’s often easier to count the number of things in the complement and then subtract....
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