Consider a situation where the order matters and a situation where the order does not matter.
See solution.
Practice makes perfect
We are asked to describe a situation where the number of possibilities are given by the permutations of 5 objects taken 2 at a time. We are also asked to describe a situation where the number of possibilities is given by the combinations of 5 objects taken 2 at a time. Let's begin with the permutations! Keep in mind that both situations are only examples, and there are many other possible answers.
Permutations
Suppose that we have 5 new books. Consider that we only have space in a bookshelf to display 2 new books. Since the order of the books in display does matter, the possibilities to choose 2 of the 5 books to display in the bookshelf is given by _5P_2.
Combinations
Again, suppose that we have 5 new books. Consider that we are going to travel and that we can only take 2 books in our backpack. Since the order of the books in a backpack does not matter, the possibilities to choose 2 of the 5 books to pack is given by _5C_2.
