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Question: question 8 let n gt 2 be an integer and...

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Question 8: Let n > 2 be an integer and consider the set S = {1,2,… ,n). An ordered triple (A, x,y) is called awesome, if (i) A-S, (ii) x є A, and (iii) y є A. Let k be an integer with 1 S kn. Determine the number of awesome triples (A, , y) with IA] = k. . Prove that the number of awesome triples (A, , y) with x -y is equal to n-2-1 Determine the number of awesome triples (A, , y) with rfy. Use the above results to prove that k= 1

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