Question 162961
*[Tex \LARGE \textrm{_{n}C_{r}=]{{{n!/(n-r)!r!}}} Start with the given formula




*[Tex \LARGE \textrm{_{12}C_{0}=]{{{12!/(12-0)!0!}}} Plug in {{{n=12}}} and {{{r=0}}}




*[Tex \LARGE \textrm{_{12}C_{0}=]{{{12!/12!0!}}}  Subtract {{{12-0}}} to get 12



Expand 12!
*[Tex \LARGE \textrm{_{12}C_{0}=]{{{(12*11*10*9*8*7*6*5*4*3*2*1)/((12*11*10*9*8*7*6*5*4*3*2*1)0!)}}}




*[Tex \LARGE \textrm{_{12}C_{0}=]{{{(cross(12*11*10*9*8*7*6*5*4*3*2*1))/(cross(12*11*10*9*8*7*6*5*4*3*2*1))0!}}}  Cancel out the common terms




*[Tex \LARGE \textrm{_{12}C_{0}=]{{{(1)/0!}}}  Simplify



Expand 0! Note: by definition {{{0!=1}}}


*[Tex \LARGE \textrm{_{12}C_{0}=]{{{(1)/(1)}}}




*[Tex \LARGE \textrm{_{12}C_{0}=]{{{1}}} Reduce



So the answer is d) 1



Think of it this way: how many ways can you assemble a team of 0 people if you have 12 people to choose from (order does not matter)? The answer is 1 since there is only one way to do this.