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6. Let $(nk?)$ denote the number of subsets $A?[n]$ such that $?A?=k$. (a) Prove that $(nk?)k=n(n?1k?1?)$ by determining, with two different construction processes, the cardinality of the collection of subsets of $[n]$ of cardinality $k$ where one of the elements in the subset has been highlighted. (b) Use the formula from part (a) and induction to show that $(nk?)=k!(n?k)!n!?$

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