How many distinguishable arrangements

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need. Add comment. This problem can be understood through permutations, while also accounting for the fact that identical letters cannot be distinguished from one another. Good luck! Related questions At a restaurant, you can choose from 2 appetizers, 4 main courses, and 3 desserts. How many In general, if you have m items of one type and n things of another type, how many possible You have created a random 5-digit password for your computer.

A hacker tries to break in to In how many ways can you arrange 5 books in a bookshelf? Let's take a look at another example that involves counting distinguishable permutations of objects of two types. We are again dealing with arranging objects that are not all distinguishable. We couldn't distinguish among the 4 I's in any one arrangement, for example. In this case, however, we don't have just two, but rather four, different types of objects. In trying to solve this problem, let's see if we can come up with some kind of a general formula for the number of distinguishable permutations of n objects when there are more than two different types of objects.

Let's take a look at a few more examples involving distinguishable permutations of objects of more than two types. Fifteen 15 pigs are available to use in a study to compare three 3 different diets. Each of the diets let's say, A, B, C is to be used on five randomly selected pigs. In how many ways can the diets be assigned to the pigs?

Well, one possible assignment of the diets to the pigs would be for the first five pigs to be placed on diet A, the second five pigs to be placed on diet B, and the last 5 pigs to be placed on diet C.

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