Question 230050
Because you are "choosing" people to go on a trip and not to specific positions, this is a COMBINATION.  The answer for choosing 3 people out of 10 is C(10,3).  This can be calculated with an ordinary calculator (as simple as a TI30!), or by ordinary calculation.  


The simple way to do this is to make a fraction whose numerator and denominator each have a product of 3 numbers.  In the numerator start with 10 and count down 3 numbers.  In the denominator start with 3 and count down to 1:


{{{C(10,3) = (10*9*8)/(3*2*1) }}}
{{{C(10,3)=720/6=120}}}


Dr. Robert J. Rapalje