How many ways can a president and vice president be chosen from 12 active members in math club

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I understand the concept of combinations and permutations. However, I am not getting how to apply the formulas. I believe understanding exactly how to do this would help.

A club has 24 members. a. In how many ways can 4 officers, a president, vice-president, secretary and treasurer be chosen from the members of the club? b. In how many ways can a 4-person committee be chosen from the members of the club?

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Algebra ->  Permutations -> SOLUTION: a club member has 12 members. in how many ways can a president, vice president, and a secretary be chosen?... is it 12X11X10      Log On

Denise H.

asked • 09/15/14

In how many ways can a president and vice president be selected from a club consisting of 12 people? (Assume that theses 2 positions cannot be occupied by the same person)

2 Answers By Expert Tutors

president = A, vice president = B

president = B, vice president = A

are both acceptable, then what we have is a permutation question.

How many permutations are there of 12 men taken 2 at a time.

We use the formula for permutations of n things taken r at a time

! is the factorial symbol

Substituting 12 for n and 2 for r, we have

12! / 10! = 12 x 11 = 132

Hakim W. answered • 09/15/14

Highly-Experienced Award-Winning Teacher for All Areas of Mathematics

Imagine we have two slots representing the number of options for president and vice-president (respectively) out of our 12-person club:

For president, we have 12 possible options:

Once we've decided on a president, we now only have 11 possible people to choose from for vice-president:

Multiplying these options together gives us:

12*11 = 132 possible ways to choose President and Vice-President