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Chapter 8: Problem 65

Explain how to distinguish between permutation and combination problems.

Short Answer

Expert verified
Permutations are about arrangements where order matters and combinations are about selections where order doesn't matter. To distinguish, consider whether the order or sequence of objects is of significance in the problem.

Step by step solution

01

Understand permutations

A permutation is an arrangement of objects in a specific order. The order is important and would be considered to create different permutations. For example, the permutations of 'abc' are: abc, acb, bac, bca, cab and cba. So, if a problem involves an order or arrangement where sequence matters, it can be categorized as a permutation.
02

Understand combinations

A combination is a selection of objects without regard to the order. The order is not important and wouldn't be considered a different combination. For example, the combinations of 'abc' taken two at a time are: ab, ac and bc. So, if a problem involves grouping or selection where sequence doesn't matter, it can be categorized as a combination.
03

Break down the problem

To decide whether a problem is a permutation or combination problem, look at what is being asked. If the problem is asking for the number of ways to arrange or order a number of items, then it's most likely a permutation problem. If the problem is asking for the number of ways to select items, and order does not matter, then it's most likely a combination problem.

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Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (y-3)^{4} $$

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