Question 149387

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{_{25}P_{4}=]{{{25!/(25-4)!}}} Plug in {{{n=25}}} and {{{r=4}}}




*[Tex \LARGE \textrm{_{25}P_{4}=]{{{25!/21!}}} Subtract {{{25-4}}} to get 21




Expand 25!
*[Tex \LARGE \textrm{_{25}P_{4}=]{{{(25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)/21!}}}




Expand 21!
*[Tex \LARGE \textrm{_{25}P_{4}=]{{{(25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)/(21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)}}}




*[Tex \LARGE \textrm{_{25}P_{4}=]{{{(25*24*23*22*cross(21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1))/(cross(21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1))}}}  Cancel like terms.




*[Tex \LARGE \textrm{_{25}P_{4}=]{{{25*24*23*22}}}  Simplify





*[Tex \LARGE \textrm{_{25}P_{4}=]{{{303600}}}  Now multiply 25*24*23*22 to get 303,600



So 25 choose 4 (where order does matter) yields 303,600 unique combinations