Question 895187: Decide whether you would use a permutation, a combination, or neither. Next, write the solution using permutation notation or combination notation, if possible, and, finally, answer the question.
A club with 33 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many ways can this be done?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if you only wanted to elect 5 officers and you didn't care what position each one filled, then it would be a combination because order or position would not be important.
since you also want to determine who will be president, who will be vice president, etc., then order or position is important and you would use the permutation formula.
the combination formula is C(n,x) = n! / (x! * (n-x)!)
the permutation formula is P(n,x) = n! / (n-x)!
the relationship between the two formulas is as follows:
P(n,x) = C(n,x) * x!
C(n,x) = P(n,x) / x!
the formula of C(33,5) gets you 237336 combinations.
the formula of P(33,5) gets you 28480320 permutations.
5! is equal to 120
C(33,5) = P(33,5) / x! = 28480320 / 120 = 237336
P(33,5) = C(33,5) * x! = 237336 * 120 = 20480320
your answer is P(33,5) because order or position is important.
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