Chapter 1 – Counting Techniques

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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