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# HW4 - that the three numbers are all diﬀerent 3(2 points...

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Name: Math 100 Due Wednesday, October 31, 2:00 pm Homework 4 1. (2 points) How many whole numbers, between 1 and 1000, satisfy all of the following conditions: The number is odd. The number is a multiple of 3. The number is not a multiple of 7. Please use inclusion/exclusion to solve this problem. 2. (2 points) Suppose that 3 numbers are chosen independently, at random, between 1 and 100. What is the probability that the three numbers are “pairwise distinct” – in other words, what is the probability
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Unformatted text preview: that the three numbers are all diﬀerent? 3. (2 points) Suppose that n is a positive integer. Let S be a set with 2 n elements. Prove that if n > 1, then Sub ( S,n ) > 2 n . 4. (2 points) (Challenge!) Suppose that n is a positive integer. Let S be a set with 2 n elements. How many ways are there to partition S into n pairs. In other words, how many ways are there to choose n pairs from the set S , such that every member of S is a member of exactly one pair?...
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