Question 1188415
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Let's focus on the first two slots for now. The order matters because the chairperson is different from the secretary. 


We have 20 choices for the chairperson, then 19 choices for the secretary. That yields 20*19 = 380 permutations. Each time we arrive at a new seat, we count down by 1. Let A = 380 since we'll use it later.


Once we've filled those two slots, we have two additional seats where order does <u>not</u> matter. Both refreshment cleanup people have the same role/job. 


We have 18 choices for the third slot and 17 choices for the fourth slot. That gives 18*17 = 306 permutations. However, order doesn't matter so we divide by 2 to get 306/2 = 153. This represents the number of ways to pick the remaining two spots on the committee. Let B = 153.


Overall, we have A*B = 306*153 = 58140 different ways to select the four person committee.


Answer: 58140
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