Proofreading probability

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There are 5 women and 6 men in a bus. But there are only 4 seats.

Assume that all the seats will be occupied and all possible seating arrangements have the same probability to appear.

What is the probability that 2 or more men will have seats?

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Probability method gets the final probability by multiplying several fractions of probability together.

**P method**:

This method considers each seat one by one: what is the probability that this seat will get, for example, an M?

Let be the number of men that will have seats. Also, instead of writing , we use the standard notation .

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Statistics method gets the final probability by dividing the number of ways of getting the desired result by the number of all possible results.

**S method 1**:

This method considers all the seats at once: what is the number of ways that they will get, for example, 3F and 1M?

In other words, instead of the seats, this method focuses on the people: what is the number of ways that 3F and 1M will be chosen?

In other words, instead of the choosing process, this method focuses on counting the **results** of the choosing.

Let = the number of ways of …

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**S method 2**:

This method considers each seat one by one: what is the number of ways that this seat will get, for example, an M?

In other words, instead of the results, this method focuses on choosing **process** itself.

Note that this method uses **permutation** instead of combination.

— Me@2021-10-02 05:18:02 PM

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2021.10.27 Wednesday (c) All rights reserved by ACHK

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