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pancakeslover
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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
 10 months ago
 10 months ago
pancakeslover Group Title
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
 10 months ago
 10 months ago

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pancakeslover Group TitleBest ResponseYou've already chosen the best response.0
a) 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?
 10 months ago

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

pancakeslover Group TitleBest ResponseYou've already chosen the best response.0
@kropot72 do you know the answers to the rest?
 10 months ago

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

wio Group TitleBest ResponseYou've already chosen the best response.2
For 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.
 10 months ago

wio Group TitleBest ResponseYou've already chosen the best response.2
d) is very simple, number of way E will serve.
 10 months ago

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

wio Group TitleBest ResponseYou've already chosen the best response.2
Could you explain that better? I'm not sure how you got that.
 10 months ago

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

wio Group TitleBest 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
 10 months ago

wio Group TitleBest ResponseYou've already chosen the best response.2
c) 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
 10 months ago

wio Group TitleBest ResponseYou've already chosen the best response.2
d) 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
 10 months ago

wio Group TitleBest ResponseYou've already chosen the best response.2
e) 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
 10 months ago

pancakeslover Group TitleBest ResponseYou've already chosen the best response.0
thanks @wio !
 10 months ago
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