In Florida, juries for certain types of trials are made up of 6 people, and the decision must be unanimous. Suppose a jury pool consists of 17 people....

In Florida, juries for certain types of trials are made up of 6 people, and the decision must be unanimous. Suppose a jury pool consists of 17 people. In today's jury pool, there are 10 men and 7 women.

a) How many different juries of 6 are there, not taking gender into account?

b) How many different juries of 6 people are made up of only women? 

c) How many different juries of 6 people are made up of only men?

d) How many different juries of 6 people are made up of 3 men and 3 women?

e) How many different juries of 6 people are made up of at least one woman?

Hint: In this case, "at least one" means one, or two, or three, or four, or five, or six. There is a short cut to the calculations like this. In counts, N(at least one woman in a jury) = N(all possible groups) - N( no women in a jury).

f) How many different juries of 6 people are made up of at least one man?

g) How many different juries of 6 people are made up of a majority of women?

h) How many different juries of 6 people are made up of a majority of men?