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Chapter 10: Problem 79

Explain how to distinguish between permutation and combination problems.

Short Answer

Expert verified
Permutations and combinations are both ways to represent the total possible outcomes of a scenario, but they differ in whether the order of those outcomes matters or not. In permutations, order is important, and in combinations, it's not. To determine which one to use in a given problem, consider whether the order of the outcomes matters. If it does, use permutations. If it doesn't, use combinations.

Step by step solution

01

Define Permutations

Start by defining permutations. Permutations refer to the arrangement of objects, where the order is important. They are used when the order of items or events matters. For example, if you are tasked with figuring out the different ways to arrange books on a shelf, you would use permutations.
02

Define Combinations

Next, define combinations. Combinations refer to the selection of objects, where the order doesn't matter. They are used when you just need to figure out how many ways you can choose a certain number of items from a larger group, regardless of order. If, for example, you need to identify the number of ways to form a committee from a larger group of people, you would use combinations.
03

Identify key differences

The key difference between permutations and combinations lies in the importance placed on order. In permutations, order matters, while in combinations, order doesn't matter. Therefore, when presented with a problem, consider whether the order of the events or items matter or not. If they do, it's a permutations problem. If they don't, it's a combinations problem.

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