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The total number of permutations of $n$ elements taken $m$ at a time
(symbol $V_n^m$) is
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\[ V_n^m = \prod_{i=0}^{m-1}(n-i) = 
  \underbrace{n(n-1)(n-2)\ldots(n-m+1)}_{\mbox{total of $m$ factors}} =
  \frac{n!}{(n-m)!} \]
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