In how many ways can a president and vice president be selected from a club consisting of 12 people?

Question

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)

Answer 1

If we assume that

president = A, vice president = B

and

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

n! / (n - r)!

 

Substituting 12 for n and 2 for r, we have

12! / 10! = 12 x 11 = 132

 

132 is your answer

Answer 2

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:

 

12 _

 

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

 

12 11 

 

Multiplying these options together gives us:

 

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