Please help explain these questions

Question

a.What is a permutation of a set of distinct objects?

b. How many permutations of a set five distinct objects taken three at a time are there?

Answer 1

A permutation is the number of ways a set of items can be selected from a larger set. The order in which they are chosen counts too. In a combination, the order doesn't matter. For example, you can choose any 2 colors from 4 different colors in 6 ways (combination), but each pair could be chosen in 2 different ways if the order was important, making a total of 12 (permutation).

 

5!/(5-3)! = means 5*4*3*2*1/ 2*1 = 60 permutations. (If the order wasn't important, then it would only be 10 combinations, because each set of 3 can be ordered in 6 different ways).