How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F.

In total, permutations of three items can be selected from a group of six distinct elements.

In particular, there are ways to order three distinct items.

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Step-by-step explanation:

The formula gives the number of ways to select and order items from a group of distinct elements.

To select and order three items from a group six distinct elements, let and . Apply the formula:

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In other words, there are unique ways to select and order three items (select a permutation of three items) from a group of six distinct elements.

Consider: what's the number of ways to order three distinct items? That's the same as asking: how many ways are there to select and order three items from a group of three distinct elements? Let and . Apply the formula for permutation:

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To find the permutations, start by selecting one element as the first of the list. A tree diagram might be helpful. Refer to the attachment for an example.