Question 116147

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




*[Tex \LARGE \textrm{_{11}P_{3}=]{{{11!/(11-3)!}}} Plug in {{{n=11}}} and {{{r=3}}}




*[Tex \LARGE \textrm{_{11}P_{3}=]{{{11!/8!}}} Subtract {{{11-3}}} to get 8




Expand 11!
*[Tex \LARGE \textrm{_{11}P_{3}=]{{{(11*10*9*8*7*6*5*4*3*2*1)/8!}}}




Expand 8!
*[Tex \LARGE \textrm{_{11}P_{3}=]{{{(11*10*9*8*7*6*5*4*3*2*1)/(8*7*6*5*4*3*2*1)}}}




*[Tex \LARGE \textrm{_{11}P_{3}=]{{{(11*10*9*cross(8*7*6*5*4*3*2*1))/(cross(8*7*6*5*4*3*2*1))}}}  Cancel like terms




*[Tex \LARGE \textrm{_{11}P_{3}=]{{{11*10*9}}}  Simplify





*[Tex \LARGE \textrm{_{11}P_{3}=]{{{990}}}  Now multiply 11*10*9 to get 990



So 11 choose 3 (where order does matter) yields 990 unique combinations