5. Does order matter?

good work I left you with this question why are there exactly six combinations of each cast when you select three actors from a group of four to get a feeling for what's up let's look at the first two boxes notice that in the first cast or box we have all possible orderings of a B and C mathematicians call each of these orderings a permutation now the number of permutations is represented by the number of rows in each box the same is true in the second cast involving a B and D how many orderings or permutations are there of three things we saw earlier that there are three factorial or six permutations bingo that's it to keep order from mattering we need to take the total number of combinations where order does matter and divide that by all the possible permutations so when choosing three actors from for actors total we can write our calculation as four times three times two over three factorial which equals four let's do another example and figure out how many casts we can form with three actors from a pool of six actors in this case there would be six times five times four we then have to again divide by three factorial to keep the order from mattering leaving six times five times four over three factorial which equals 20 so there are 20 different casts in this case use the next exercise to get some practice with some other examples and perhaps you'll recognize our good friend moe in the cast