[3 marks each] Use a combinatorial argument to prove each of the following identities. No marks...

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[3 marks each] Use a combinatorial argument to prove each of the following identities. No marks will be awarded for use of any other method. (a) () () = (m) (Rm) (Hint: Use a committee selection argument where you also select a subcommittee.) (b) 1() +2(2) + 3(3) + ... + n(n) + n(n) = n. 2n-1 (Hint: Use a committee selection argument where your committee can be any size, but it must contain a president.) [3 marks each] Use a combinatorial argument to prove each of the following identities. No marks will be awarded for use of any other method. (a) () () = (m) (Rm) (Hint: Use a committee selection argument where you also select a subcommittee.) (b) 1() +2(2) + 3(3) + ... + n(n) + n(n) = n. 2n-1 (Hint: Use a committee selection argument where your committee can be any size, but it must contain a president.)