# HW5 - b,d,e is an ordered triple of elements of S whose...

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Math 100 Homework 5 Martin H. Weissman 1. (3 points) Let S = { a,b,c,d,e,f } . (a) How many subsets of S have 3 elements? For example, { b,d,e } is a subset of S with 3 elements. Note that { b,d,e } = { b,e,d } – order does not matter when choosing a subset. (b) How many ordered triples are there whose entries are elements of S ? For example, ( b,d,e ) is an ordered triple whose entries are elements of S . Note that ( b,d,e ) 6 = ( b,e,d ) – order does matter when choosing an ordered triple. Also, note that that ( b,b,e ) is an ordered triple – ordered triples can have repeated elements. (c) How many ordered triples are there, whose entries are elements of S , such that all entries are distinct? For example, (
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Unformatted text preview: b,d,e ) is an ordered triple of elements of S , whose entries are distinct. However ( b,b,e ) does not have distinct entries. 2. (1 point) Prove that, if n is a natural number, and n ≥ 4, then n 2 ≥ 5 n-7. 3. (2 points) Let A n be the sequence deﬁned by the following: • Let A = 1. • For all positive integers n , let A n = 3 A n-1-n . Prove that, for every natural number n , A n ≤ 3 n-n 2 . 4. (2 points) Let N be the (large) positive integer: N = 3 3 · 7 3 · 11 7 . How many numbers between 1 and N (inclusive) are factors of N ?...
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