Unformatted text preview: * 4 + 3 * 3 mod 4, one may do: 2 * 4 + 3 * 3 mod 4 = (8) + (9) mod 4 = 17 mod 4 = 1 mod 4 , rather than: 2 * 4 + 3 * 3 mod 4 = (0) + (1) mod 4 = 1 mod 4 . Is it okay to produce numbers larger than the mod we are working in and if so why? 4. How many ways can one write seven as the sum of four nonnegative integers? (Note: Order does not matter, 6+1+0+0 is the same as 0+0+1+6, don’t count it twice.) 5. (a) Roll a k-sided dice, three times: How many possible outcomes are there? What is the probability of a face appearing exactly two times? (b) Roll a 6-sided dice three times: What is the probability of each face being diﬀerent in three rolls? What is the probability of a face appearing exactly two times? What is the probability of a face appearing three times? What is the sum of the above three probabilities? 1...
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This note was uploaded on 11/11/2011 for the course CS 2800 at Cornell.