Q:

In how many ways can you arrange six things?

A:

Quick Answer

There are 720 ways in which six things can be arranged. The number of ways that a set of things can be arranged is known as the number of permutations of that set. Each distinct arrangement is called a permutation.

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In how many ways can you arrange six things?
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Full Answer

Permutations are computed using factorials. A factorial is a product of a number and all the numbers below it. The factorial of a number is represented in shorthand using an exclamation point. For instance, 6! Is the factorial of 6.

Thus, a set of six things can be arranged in (6*5*4*3*2*1) ways, which works out to 720 ways.

Generally, n! is the number of permutations of “n” things, whereas n!/r! is the number of permutations of “n” things where “r” of them are repeated. When a set contains repeated elements, the order in which those elements are arranged is important and they can only be arranged in a permutation rather than a combination.

If a set contains only unique elements, then order does not matter and in that case, a combination is used. Combinations are groups of numbers that are combined to form a set. Typically, there are fewer combinations than permutations.

In short, permutations are used to arrange items in a list, whereas combinations are used for group items.

In real life, permutations and combinations have several applications, such as finding the number of ways that an event can take place, finding lock codes and calculating possible lottery combinations.

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