Problem

Evaluate the following permutation.
\[
{ }_{22} P_{2}
\]

Answer

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Answer

Final Answer: The permutation of 22 items taken 2 at a time is \(\boxed{462}\).

Steps

Step 1 :We are given a permutation problem to solve, where we need to evaluate the permutation of 22 items taken 2 at a time. The permutation is denoted as \({ }_{22} P_{2}\).

Step 2 :The formula for permutation is given by \(nPr = \frac{n!}{(n-r)!}\), where \(n\) is the total number of items, \(r\) is the number of items to choose, and \(n!\) is the factorial of \(n\).

Step 3 :In this case, \(n = 22\) and \(r = 2\). So, we need to calculate \({ }_{22} P_{2} = \frac{22!}{(22-2)!}\).

Step 4 :After calculating, we find that the permutation of 22 items taken 2 at a time is 462.

Step 5 :Final Answer: The permutation of 22 items taken 2 at a time is \(\boxed{462}\).

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