help with question. I dont understand the differences.

Question

What is the difference between the C and P? The only thing I could think of is P stands for probability but no idea what C stands for. I believe it will be either B or C since there is only one way for the truck to visit them in reverse alphabetical order.

 

A delivery truck must make stops in eight different cities, designated by the first letter in the name of the city: A, B, C, D, E, F, G, and H. If the order in which the truck visits the eight locations is chosen randomly, what is the probability that the truck will visit them in reverse alphabetical order?

 

a. 8C1/8P1

b. 1/8P8

c. 1/8C8

d. 8P1/8C1

 

Answer 1

P stands for Permutation and C stands for Combination.  Both relate to ordering object for selection purposes.  If the order of selection is important, meaning it does matter if something comes first like people finishing a race or placing books on a shelf, then you use P (Permutation).  If the order doesn't matter, if you are more concerned with the members of a group and not the order they were selected (for example, pizza toppings (pepperoni and sausage is the same as sausage and pepperoni)), then you use C (combination).

 

Since it is rare to mix and match (either order is important or it isn't), options A and D are eliminated.  The order the truck stops in each city is important, so we'd use P (permutation) to calculate.  (Option B)

 

(FYI: the probability calculated is 1/40320).