Question 94372
Since order does matter, we must use the <a href=http://www.mathwords.com/p/permutation_formula.htm>permutation formula</a>:





*[Tex \LARGE \textrm{_{n}P_{r}=]{{{n!/(n-r)!}}} Start with the given formula




*[Tex \LARGE \textrm{_{8}P_{8}=]{{{8!/(8-8)!}}} Plug in {{{n=8}}} and {{{r=8}}}




*[Tex \LARGE \textrm{_{8}P_{8}=]{{{8!/0!}}} Subtract {{{8-8}}} to get 0




Expand 8!
*[Tex \LARGE \textrm{_{8}P_{8}=]{{{(8*7*6*5*4*3*2*1)/0!}}}




Expand 0! to get 1
*[Tex \LARGE \textrm{_{8}P_{8}=]{{{(8*7*6*5*4*3*2*1)/(1)}}}





*[Tex \LARGE \textrm{_{8}P_{8}=]{{{8*7*6*5*4*3*2*1}}}  Simplify





*[Tex \LARGE \textrm{_{8}P_{8}=]{{{40320}}}  Now multiply 8*7*6*5*4*3*2*1 to get 40,320



So 8 choose 8 (where order does matter) yields 40,320 unique combinations