Question 787015
SOCIAL STUDIES NOTE:
This maybe a good probability problem, but it would probably make most Social Studies teachers cry.
The US Senate has 100 members, 2 for each of the 50 states.
Maybe a committee of the Senate would be a small as 13+18=21 members.
It would be hard to find 13 women in a Senate committee with 21 members, because we only have 20 women among the 100 Senators.
 
MATH:
Use combinations.
a. There are
{{{(matrix(2,1,31,5))=31*30*19*28*27/(5*4*3*2)=highlight(169911)}}} ways to select 5 people from a group of 13+18=31 people
 
b. There are {{{(matrix(2,1,13,2))=13*12/2=78}}} ways to select 2 women from a group of 13 women.
There are {{{(matrix(2,1,18,3))=18*17*16/(3*2)=816}}} ways to select 3 men from a group of 18 men.
So, there are {{{78*618=63648}}} ways to select a subroup made of 2 women and 3 men from a group of 13 women and 18 men.
Since there is a total of 169911 different subgroups of 5 people that could be formed from the same group of 13 women and 18 men, the probability of one of those  subgroups being one of the 78 with exactly 2 women is
{{{63648/169911=about0.3746}}} (or about 37.46%).
 
DISCLAIMERS:
I never was a Socials Studies teacher, and never even tried to be a teacher, but I did learn about US Government once.
I would like to live to see the day that 13 out of every 31 US Senators are women, but we are still far from that ratio.