Unformatted text preview: { a,c } . 6. Suppose that S is a set with 6 elements. How many subsets does S have with 3 elements? There are 20 subsets of S with 3 elements, since (6!) / (3!3!) = 20. 7. Suppose that S is a set with 5 n elements. How many subsets of S have 2 n elements? There are (5 n )! (2 n )!(3 n )! subsets of S with 2 n elements. 8. Suppose that S is a set with 6 elements. How many subsets of S have an even number of elements? There are 32 subsets of S with an even number of elements, since 32 = 2 61 . 9. Suppose that S is a set with 10 elements. How many ordered pairs are there, whose entries are elements of S ? There are 100 ordered pairs with entries in S , since 100 = 10 2 . 10. Let S be the set of pairs ( a,b ), such that 1 ≤ a ≤ 100, 1 ≤ b ≤ 100, and a + b = 101. How many elements does S have? S has 100 elements....
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This note was uploaded on 04/17/2008 for the course MATH 100 taught by Professor Weissman during the Fall '08 term at UCSC.
 Fall '08
 Weissman
 Sets

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