The answer is 10/143.
The probability that the first person is a man is 8/14 (because there are 8 men among 14 people).
The probability that the second person is also a man is 7/13 (because there are 7 men (one has already arrived) among 13 people (because one has already arrived).
The probability that the third person is also a man is 6/12.
The probability that the fourth person is also a man is 5/11.
Because all these events occur together, we will use the multiplication rule and multiply the probabilities.
Thus, the probability that the first 4 people to show up are men is:
[tex]\frac{8}{14} * \frac{7}{13} * \frac{6}{12} * \frac{5}{11} = \frac{8*7*6*5}{14*13*12*11} = \frac{1680}{24024} = \frac{168*10}{168*143} = \frac{10}{143} [/tex]
