Algebra

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 31 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many ways can this be done?
I came up with 155 ways,
Thank you and Good afternoon

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  1. It is not combinations because the order matters, it is permutations. (Joe could be either president or vice president for example and those are not the same)
    31!/(31-5)!
    = 31!/26!
    = 31*30*29*28*27
    = 20,389,320

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    posted by Damon
  2. thank you Damon I took notes to see how if falls into place.

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  3. You are welcome.
    This is a good example to diiferentiate between combinations and permutations

    Combinations of 31 taken 5 at a time would be
    31! /[ 5! (31-5)! ]

    That takes into account all the different groups of five you can make, but does not order the five for specific office.

    If you now require a different choice for every office within the group of 5, you will get 5! or 120 times as many arrangements
    20,389,320 / 120 = 169,911
    so I do not know where you got 155

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    posted by Damon

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