Question 195136
I'm assuming that order doesn't matter.



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{_{9}C_{5}=]{{{9!/(9-5)!5!}}} Plug in {{{n=9}}} and {{{r=5}}}




*[Tex \LARGE \textrm{_{9}C_{5}=]{{{9!/4!5!}}}  Subtract {{{9-5}}} to get 4



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



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




*[Tex \LARGE \textrm{_{9}C_{5}=]{{{(9*8*7*6*5*cross(4*3*2*1))/(cross(4*3*2*1))5!}}}  Cancel




*[Tex \LARGE \textrm{_{9}C_{5}=]{{{(9*8*7*6*5)/5!}}}  Simplify



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




*[Tex \LARGE \textrm{_{9}C_{5}=]{{{15120/(5*4*3*2*1)}}}  Multiply 9*8*7*6*5 to get 15,120




*[Tex \LARGE \textrm{_{9}C_{5}=]{{{15120/120}}} Multiply 5*4*3*2*1 to get 120




*[Tex \LARGE \textrm{_{9}C_{5}=]{{{126}}} Now divide




So 9 choose 5 (where order doesn't matter) yields 126 unique combinations