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2sally2
02.02.2021 •
Mathematics
A survey of 200 recent high school graduates found that 170 had driver licenses and 108 had jobs. 21 graduates said that they had neither a driver license nor a job.
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Ответ:
Step-by-step explanation:
Intro:We can use probability functions here to try and solve this problem.
We want to find how many ways to choose a senator from a chosen state. Note the "from a chosen state," meaning that it is not asking for how many ways to choose two senators from all 50 states but how to choose 1 from a chosen state (1 chosen state).
Let's calculate all possible values for each scenario.
Choosing a senator from one state:We can either chose Senator A or Senator B for one state, since there are only two options available
This gives us a total of two possibilities to choose a senator from one state.
Choosing 3 states to be representedThe number of ways to choose 3 states being represented, we can use the combinations formula. We can write it as ₅₀C₃, which can be solved using the formula:
Where n is the total number of objects to choose from, and r is how many we want to choose.
Substituting in:
Hence, there are 19,600 ways to choose 3 states from 50 total.
Choosing a 3 member committeeThe total number of possible combinations to choose three senators from 50 states, none of the states being equal, we can multiply the number of ways to pick 3 states from 50 (19600) and multiply it by
since there are 3 members in the Senate and two Senators in each state.
Hence, there are 156,800 ways to make a 3-senator committee with no member from the same state (2 senators per state).
Conclusion:However, let's look back at what the problem is asking.
"How many ways can we choose a Senator from a chosen state?"
Put simply - assuming we chose a state, how many ways can we select a senator from that state?
We answered that in Part 1! We ended up getting two ways, as there are two senators.
Therefore, the answer to your problem is 2 ways.
Hope this helped!