It took me several readings to understand the problem,
. . but I think I've got it now.
With no gender bias, we have these possible votes:The board of 8 members, 5 women and 3men,
received a complaint about sex discrimination
and they voted 5-3 in favour of the plaintiff.
The attorney representing the company appealed the board's decision
by claiming sex bias on the part of the board members.
If there were no sex bias among them, it might be reasonable to say that
any group of 5 members would be as likely to vote for the complainant.
If this were the case, what is the probability that the vote would split along sex lines?
. . . . . . . . . . . . . . .
There are 56 ways that the vote could be split, all equally likely.
There is one way that is split along sex lines.