Math 55 Worksheet July 19, 2011 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 2. How many strings of 5 decimal digits (a) contain at least one 4? (b) do not contain the same digit twice? (c) do not have two consecutive symbols that are the same?
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