Four customers are to be chosen for prizes 123 and 4th plac

. Four customers are to be chosen for prizes 1,2,3, and 4th place out of a set of 25 different customers.

a) How many possible combinations are there for the four winners, in which all we care about is whether the person was chosen at all, not in what position they finished?

b) How many different orderings of the top 4 would be possible (order does matter)?

Solution

a)

First is a combination

From 25 people, you selct 4 people for prizes.

25C4 = 12650

b)

Second is a permutation because even the order of prizes matters

25P4 = 303600