In 5 different cities there are 6, 4, 4, 3, 1 people who work for the same company. From these 3 are chosen to participate in a project group.

If the selection is random what's the probability that all participants are from the same city?

Question

In 5 different cities there are 6, 4, 4, 3, 1 people who work for the same company. From these 3 are chosen to participate in a project group. 

If the selection is random what's the probability that all participants are from the same city?

anonymous · Answer

all three will be from the same city only if they are drawn from first four cities.
so probability of choosing three persons from the first four cities is 
(6c3+4c3+4c3+3c3)/18c3