Five men in a group of 20 are graduates if 3 men are picked out of 20 at random i what is the probability that all graduates and ii what is the probability of at least one being graduate?

The probability that all will be graduates will be 5/20 x 4/19 x 3/18. This equals 0.0087719, or 0.877% The probability of at least one being a graduate is 1 minus the probability of none being graduates. That's 1-(15/20 x 14/19 x 13/18)

= 1 - 0.39912280701754385964912280701754

= 0.600877

=60%

Thus the probability of having at least one graduate is 60%