8men and 6 women arrive separately in a random fashion to a meeting. what is the probability that the first 4 people to show up are men?

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:

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