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 one year ago
A president, treasurer, and secretary, all different, are to be chosen, from a club consisting of 10 people. How many different choices of officers are possible if
 one year ago
A president, treasurer, and secretary, all different, are to be chosen, from a club consisting of 10 people. How many different choices of officers are possible if

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pancakeslover
 one year ago
Best ResponseYou've already chosen the best response.0a) there are no restrictions? b) A and B will not serve together? c) C and D will serve together or not at all? d) E must be an officer? e) F will only serve if he is the president?

kropot72
 one year ago
Best ResponseYou've already chosen the best response.1a) If there are no restrictions the number of choices is given by 10P3.

pancakeslover
 one year ago
Best ResponseYou've already chosen the best response.0@kropot72 do you know the answers to the rest?

wio
 one year ago
Best ResponseYou've already chosen the best response.2For b), my strategy would be to find how many ways A and B will serve together and subtract that from the total.

wio
 one year ago
Best ResponseYou've already chosen the best response.2For c) you are doing a) again but with 8 people to find out how many ways C and D are not at all serving together, then adding to what you got in b) for ways A and B will serve together.

wio
 one year ago
Best ResponseYou've already chosen the best response.2d) is very simple, number of way E will serve.

wio
 one year ago
Best ResponseYou've already chosen the best response.2e) is number of ways F doesn't serve plus number of ways to assign treasurer and secretary to remaining 9 people

wio
 one year ago
Best ResponseYou've already chosen the best response.2Could you explain that better? I'm not sure how you got that.

wio
 one year ago
Best ResponseYou've already chosen the best response.2For b) I'm getting: \[ ^{10}P_{3}  (^{3}C_{2} \times ^{8}P_{1}) \]

wio
 one year ago
Best ResponseYou've already chosen the best response.2\(^3C_2\)  ways to assign A and B a position \(^8P_1\)  ways to fill the remaining position \(^3C_2\times ^8P_1\)  ways A and B will serve together \(^{10}P_3(^3C_2\times ^8P_1)\)  ways A and B will not serve together

wio
 one year ago
Best ResponseYou've already chosen the best response.2c) C and D will serve together or not at all? \(^3C_2\times ^8P_1\)  ways C and D will server together \(^8P_3\)  ways neither C nor D will serve \((^3C_2\times ^8P_1) +^8P_3 \)  ways C and D will server together or not at all

wio
 one year ago
Best ResponseYou've already chosen the best response.2d) E must be an officer \(^3C_1\)  ways E can be an officer \(^9P_2\)  ways to fill the two remaining positions \(^3C_1 \times ^9P_2\)  ways E is an officer

wio
 one year ago
Best ResponseYou've already chosen the best response.2e) F will only serve if he is the president? \(^1C_1\)  ways F is president \(^9P_2\)  ways to fill remaining two seats \(^9P_3\)  ways F will not server \((\ ^1C_1\times\ ^9P_2\ )+^9P_3 \)  ways if is president or does not serve
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