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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
 7 months ago
 7 months 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
 7 months ago
 7 months ago

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pancakesloverBest 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?
 7 months ago

kropot72Best ResponseYou've already chosen the best response.1
a) If there are no restrictions the number of choices is given by 10P3.
 7 months ago

pancakesloverBest ResponseYou've already chosen the best response.0
@kropot72 do you know the answers to the rest?
 7 months ago

wioBest 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.
 7 months ago

wioBest 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.
 7 months ago

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

wioBest 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
 7 months ago

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

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

wioBest 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
 7 months ago

wioBest 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
 7 months ago

wioBest 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
 7 months ago

wioBest 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
 7 months ago
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