We want to find a word to complete the given sentence.
An arrangement of objects in which the order is important is called a(n) ___________.
A permutation is an arrangement of objects in which the order is important. Consider that we have three marbles — a blue marble, an orange marble, and a green marble. Now we will look at every different arrangement we can make with these marbles. Let's start with blue, green, and then orange!
We can see that, even when we have the same three marbles, we can make six different arrangements depending on which position each marble has. These arrangements are the permutations of the three marbles. We can use the Fundamental Counting Principle to find the permutations of three objects.
Notice that, if we choose the blue marble to be in the first position, we cannot choose it for the second position. This is why the number of choices is reduced with each position. There is also a general formula to find the permutations of n objects taken r at a time.
_nP_r = n!/( n- r)!
In this formula, each exclamation point represents the factorial of the value before the exclamation point. Let's complete the sentence.
An arrangement of objects in which the order is important is called a permutation.
