Question 90525


Since order does matter, we can 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{_{6}P_{4}=]{{{6!/(6-4)!}}} Plug in {{{n=6}}} and {{{r=4}}}




*[Tex \LARGE \textrm{_{6}P_{4}=]{{{6!/2!}}} Subtract {{{6-4}}} to get 2




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




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




*[Tex \LARGE \textrm{_{6}P_{4}=]{{{(6*5*4*3*cross(2*1))/(cross(2*1))}}}  Cancel




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





*[Tex \LARGE \textrm{_{6}P_{4}=]{{{360}}}  Now multiply 6*5*4*3 to get 360



So 6 choose 4 (where order does matter) yields 360 unique combinations