Two people are selected at random from a group of 6 pilots and 4 engineers. What is the probability that both of them are engineers?

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number of choices of any 2 of the 10
= C(10,2) = 45
number of choices of any 2 of the 4 engineers
= C(4,2) = 6
Prob(of stated event) = 6/45 = 2/15

or, simply

prob(of stated event) = (4/10)(3/9) = 2/15