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(Solved): 6. Let (nk) denote the number of subsets A[n] such that A=k. (a) Prove that (nk)k=n ...



6.
Let \( \left(\begin{array}{l}n \\ k\end{array}\right) \) denote the number of subsets \( A \subseteq[n] \) such that \( |A

6. Let denote the number of subsets such that . (a) Prove that by determining, with two different construction processes, the cardinality of the collection of subsets of of cardinality where one of the elements in the subset has been highlighted. (b) Use the formula from part (a) and induction to show that


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Explanation:(a) To prove that (n k )k=n(n?1 k?1 ) we will determine the cardinality of the collection of subsets of [n] of cardinality k where one of
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