Question 145216
Start off with a simpler problem where the principle is the same.
Suppose there are a group of 3 candidates to be chosen from 7
applicants. Now write out the possible choices
A,B,C,D,E,F,G are the candidates
Here's all the ones that include A
ABC ACD ADE AEF AFG
ABD ACE ADF AEG
ABE ACF ADG
ABF ACG
ABG
Without repeating myself, heres the ones that include B
BCD BDE BEF BFG
BCE BDF BEG
BCF BDG
BCG
Without repeating myself, heres the ones that include C
CDE CEF CFG
CDF CEG
CDG
Without repeating myself, heres the ones that include D
DEF DFG
DEG
Without repeating myself, heres the ones that include E
EFG
----------------------
These add up to 35 choices
The formula for combinations from 7 chosen 3 at a time is:
{{{7! /(3! * (7-3)!) = 35}}}
Now for your problem:
{{{19! / (7! * (19 - 7)!) = 50388}}}
Of course, I could be in error, but I hope not