How many different and can students at a school select the president, Vice President, and secretary from a group of 5 people?

A 120

B 60

C 20

D 15

When buying a new dress, you have a choice of 3 different lengths, 5 different colors, and 2 different styles. How many choices are there for one dress?

A 13

B 15

C 30

D 32

1)

P (n, k) = n (n-1) (n-2) ... (n+1-k) It's easier to write with factorials, with P (n, k) = n!/k!, but the above is easier to compute most of the time. Without that, you can still solve with common sense. There are 5 ways to pick the president. For each of those, there are 4 choices left for vice president, and for each of those there are 3 choices left for secretary. 5*4*3 = 60 total