The US Senate consists of 100 senators, 2 from each state. A group of 5 senators is formed.
1.) how many groups are possible?
2.)how many are possible if no 2 senators from the same state can be chosen?
3.)what is the probability that no 2 from the same state are chosen?
for 1.) i got 100C5, 100 choose 5
the rest im lost on how to do
For question 2, you need to consider that no two senators from the same state can be chosen. To find the number of possible groups in this scenario, you can first choose one senator from each of the 50 states. This would result in 50 senators being chosen.
Now, you need to choose 3 more senators from the remaining 50 senators (2 from each state minus the 1 already chosen). This can be done in (50C3) ways, which represents choosing 3 senators from a pool of 50 senators without replacement.
To find the total number of possible groups in this case, you multiply the number of ways to choose one senator from each state by the number of ways to choose the remaining 3 senators. Therefore, the number of possible groups, where no two senators from the same state are chosen, is given by:
(50C1) * (50C3)
For question 3, to find the probability that no two senators from the same state are chosen, you need to divide the number of groups satisfying the condition (from question 2) by the total number of possible groups (from question 1).
So, the probability is:
[(50C1) * (50C3)] / (100C5)