Question 85469
Using 

{{{nCr=n!/(n-r)!r!}}}


{{{10C3=10!/(10-3)!3!}}} Plug in n=10, r=3


{{{10C3=10!/(7)!3!}}} Subtract


{{{10*9*8*7*6*5*4*3*2*1/(7*6*5*4*3*2*1)(3*2*1)}}} Evaluate the factorials


{{{10*9*8*cross(7*6*5*4*3*2*1)/cross(7*6*5*4*3*2*1)(3*2*1)}}} Divide and cancel out like terms 


{{{10*9*8/(3*2*1)}}}


{{{720/6}}} Multiply


{{{120}}} Divide


So {{{10C3=120}}}