SOLUTION: The US Senate consists of 13 women and 18 men. If you randomly select five different senators. a. In how many possible ways can we select five senators out of this group? b. W

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Question 787015: The US Senate consists of 13 women and 18 men. If you randomly select five different senators.
a. In how many possible ways can we select five senators out of this group?
b. What is the probability that if we select five senators two of them are female?
Found 2 solutions by stanbon, KMST:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The US Senate consists of 13 women and 18 men. If you randomly select five different senators.
a. In how many possible ways can we select five senators out of this group?
Ans: 31C5 = 169911 ways
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b. What is the probability that if we select five senators two of them are female?
# of ways to succeed:: 13C2*18C3
# of possible outcomes: 169911
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P(2 female) = [63648)/169911 = 0.3746
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Cheers,
Stan H.
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Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
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
ways to select 5 people from a group of 13+18=31 people

b. There are %28matrix%282%2C1%2C13%2C2%29%29=13%2A12%2F2=78 ways to select 2 women from a group of 13 women.
There are %28matrix%282%2C1%2C18%2C3%29%29=18%2A17%2A16%2F%283%2A2%29=816 ways to select 3 men from a group of 18 men.
So, there are 78%2A618=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%2F169911=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.