Chapter 1 – Counting Techniques

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Topic 1.4

Permutations II

This lesson expands the usefulness of the permutation counting technique developed in the *Permutations – Part I* lesson to include permutations of a partial list of the full set of elements from which we are choosing. (For example, list the 1st, 2nd, and 3rd place winners in a eight horse race.) It gives the standard formula for permutations:

[latex]P(n,k) = \frac{n!}{(n-k)!}[/latex]

It is important to note that the process for counting permutations relies on the *General Counting Principle*, which involves only multiplication. The division in the formula is not natural. It is important conceptually for students to understand the underlying multiplication, and not just rely on the formula.

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