Another way to count the total number of all committees with a chair, is to consider Frst selecting the chairperson from which we have n choices and then considering all possible subsets of size n-1(wh ichis2 n - 1 )f romwhichtocon s t ru c tther ema in ingcomm i t t e e members. The product then gives n 2 n - 1 . Part (b): Consider again n people where now we want to count the total number of com- mittees of size k with a chairperson and a secretary. We can select all subsets of size k in ± n k ² ways. Given a subset of size k ,thereare k choices for the chairperson and k choices for the secretary giving k 2 ± n k ²committees of sizek with a chair and a secretary. The total number of these is then given by summing this result orn³
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