A high school sewing club has 11 members. In how many different ways can they choose a president and vice president?

a. 121

b. 110

c. 21

d. 55

Since the order matters Person A and B can be chosen as AB (A pres B vice pres) or BA (B president A Vice president)

When the order matters we are talking about permutations. How many permutations of 11 taken 2 at a time are there.

It can be written like this 11nPr 2

It means start at 11 and multiply by the next lower number

11 x 10 = 110 ways they can choose.

Extension of the concept:

If there had been three positions President, Vice President, and Treasurer

then it would be 11nPr3 or 11 x 10 x 9

Once again the answer to your problem is 110.