Question

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 29 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many ways can this be done?
ways

Answer 1

If the order in which the selection is made is important, then permutations are needed. If the order is not important, then combinations are needed. Which do you think applies in this question?

Answer 2

Do you think that if you were selecting the five officers it wouldn't matter which one was president, vice president, secretary, treasurer, or historian?

Answer 3

Or putting it another way, a voting paper would have a list of the five positions, president, vice president, secretary, treasurer, and historian. If you knew which 5 of the 29 members you wanted to vote for, wouldn't you choose specific members for each of the 5 positions. The voting paper would not allow you to just select a group of 5 unless you stated the position as an officer for each.

Answer 4

yes,

Answer 5

Therefore the order in which the selection is made is important. So, bearing in mind my first post, which applies in this question - permutations or combinations?

Answer 6

permu

Answer 7

Correct! Do you know the notation for permutations?

Answer 8

There are several different notations for permutations without repetition. Which have you been taught?

Answer 9

n p r

Answer 10

1234, 1243

Answer 11

Yes, nPr can be used for the number of permutations of n different things taken r at a time. Therefore your question can be solved using 29P5.
\[nPr=\frac{n!}{(n-r)!}\]
Can you plug the values 29 and 5 into the above formula and solve?