Consider a permutation question using the same four fruits as Example 1. What might this problem look like? A slot machine is shown below. When you pull the lever on a slot machine you hope to get all four spinners to show the same fruit to produce a win.
This is a permutation; therefore, use the Fundamental Counting Principle. Because there are four fruits, there are four choices for each spinner. The total number of ways the fruit can be shown with one spin is 4 x 4 x 4 x 4 = 256. The assumption you mare making about the slot machine is that each spinner has only the four fruits on it. Typically, this is not the case. Often a 4-spinner machine will have five or six different pictures on each spinner. This increases the number of ways the fruit can be shown, making winning more difficult! |
Although the same four fruits are used in both Example 1 and Example 2, the answer in Example 1 is significantly smaller. This will always be the case - the permutation of a group of objects is larger than the combination of the same group of objects . When order matters (permutation), there are more distinct possibilities of how to arrange the objects.