Ahigh 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.