A Club Has Seven Members

Essay

A club has seven members. Three are to be chosen to go as a group to a national meeting.
(a) How many distinct groups of three can be chosen?
(b) If the club contains four men and three women, how many distinct groups of three contain
two men and one woman?
(c) If the club contains four men and three women, how many distinct groups of three contain
at most two men?
(d) If the club contains four men and three women, how many distinct groups of three contain
at least one woman?
(e) If the club contains four men and three women, what is the probability that a distinct
group of three will contain at least one woman?
(f) If two members of the club refuse to travel together as part of the group (but each is
willing to go if the other does not), how many distinct groups of three can be chosen?
(g) If two members of the club insists on either traveling together or not going at all, How
many distinct groups of three can be chosen?