SOLUTION: A 40-member club will elect a president and elect a vice president. How many possible ways can a president and vice president be elected from this club/ Suppose the 40 member c

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 Algebra: Combinatorics and Permutations Solvers Lessons Answers archive Quiz In Depth

 Question 626167: A 40-member club will elect a president and elect a vice president. How many possible ways can a president and vice president be elected from this club/ Suppose the 40 member club instead elects two co-presidents. How many possible ways can co-presidents be elected from this club? How are these questions alike and how are they different?Answer by Theo(3556)   (Show Source): You can put this solution on YOUR website!n = 40 want to elect a president and vice president. formula is P(40,2) P is for permutation with n = 40 and x = 2. the number of possible permutation is equal to 40! / (38!) which becomes: 40 * 39 = 1560 n = 40 want to elect 2 co-presidents. formuls is C(40,2) C is for combination with n = 40 and x = 2. the number of possible combinations is equal to 40! / (38! * 2!) which becomes: 40 * 39 / 2 = 1560 / 2 = 780 the difference is in the first case order was important and in the second case order was not. this is easier to see if n = 3. you want to elect a president and vice president. the formuls now becomes P(3,2) which becomes 3! / 1! which becomes 3*2 = 6 possible ways. those ways are: ```president vice president a b a c b c b a c a c b ``` order was important because candidate A could be president or vice president. now you want to elect 2 co-presidents. the formula now becomes C(3,2) which becomes 3! / (1! * 2!) becomes 3*2/2 = 3 those ways are: ```co-president co-president a b a c b c ``` order was not important here since there is no difference between a co-president and a co-president candidate A can be one of the candidates for co-president while candidate B can be one of the candidates for co-president - which co-president position each takes doesn't matter.