A jury pool has 23 men and 17 women, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the following probabilities:
P(all men) =
P(all women) =
P(8 men and 4 women) =
P(6 men and 6 women) =
Give all answers accurate to six decimal places.