Evaluate the expression

When evaluating , you’re looking for the number of ways to arrange 0 items from a set of 6. Interestingly, the formula for permutations is given by . Plugging in our values, we get . So, there is exactly one way to arrange nothing!

It’s a curious concept but think of it this way: the empty set has only one way to exist—being empty! This idea crops up in combinatorics frequently, as it emphasizes the importance of the identity in mathematics where anything raised to the power of zero—or choosing zero items—will always equal one. So, is not just a number; it’s a wonderful principle wrapped in a neat little package.