19C5= 19! / [(19-5) ! 5 !]
The above is just an identity.
The lhs is a short way of saying "The number of combinations of 19 objects, taken 5 at a time.
The rhs is a mathematical expression giving that numerical value, and where nCr = n! / [(n-r)! * r!]
19! / [(19-5) ! 5 !] =
19! / [(14) ! 5 !] = (divide above and below by 14!)
[19*18*17*16*15] / [5!] = (expand 5!)
[19*18*17*16*15] / [5*4*3*2*1] = (cancel common factors)
[19*18*17*2] / [1] = (evaluate)
342 * 34 = 11,628
Answer: 11,628