Question 892592: Please help..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 30 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many ways can this be done?
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
Remember C stands for "Collecting" and P stands for "Positioning".
Also C stands for "Combinations" and P stands for "Permutations".
So ask this question:
Q: After selecting the 5 people, are we only COLLECTING them, or are we
POSITIONING them?
A: Since "president, vice president, secretary, treasurer, and historian"
are POSITIONS, we are POSITIONING them. So we use permutations.
So the notation is:
30 members, POSITION 5
and the notation is
30P5 or P(30,5) or 30P5 or  ,
depending on which notation your teacher uses.
Formula: Start with 30 and use 5 factors, each factor 1 less than
the previous one:
Solution: 30×29×28×27×26 = 17100720
Edwin
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