Let probability that at least one of the people chosen is a man = P(M)
So, the probability that the chosen group contains no man = 1-P(M)

1 - P(M) = Probability that all 3 are women

Probablity that first one chosen is a woman = 6/10
Probablity that second one chosen is a woman after first was a woman = 5/9
Probablity that third one chosen is a woman after first and second were women = 4/8

1 - P(M) = 6/10*5/9*4/8
P(M) = 1 - 120/720 = 1 - 1/6 = 5/6