Question 127307


Since order does not matter, we must use the <a href=http://www.mathwords.com/c/combination_formula.htm>combination formula</a>:



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




*[Tex \LARGE \textrm{_{5}C_{4}=]{{{5!/(5-4)!4!}}} Plug in {{{n=5}}} and {{{r=4}}}




*[Tex \LARGE \textrm{_{5}C_{4}=]{{{5!/1!4!}}}  Subtract {{{5-4}}} to get 1



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



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




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




*[Tex \LARGE \textrm{_{5}C_{4}=]{{{(5*4*3*2)/4!}}}  Simplify



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




*[Tex \LARGE \textrm{_{5}C_{4}=]{{{120/(4*3*2*1)}}}  Multiply 5*4*3*2 to get 120




*[Tex \LARGE \textrm{_{5}C_{4}=]{{{120/24}}} Multiply 4*3*2*1 to get 24




*[Tex \LARGE \textrm{_{5}C_{4}=]{{{5}}} Now divide




So 5 choose 4 (where order doesn't matter) yields 5 unique combinations