How many different ways of seating 4 people at a table are there? What about when one of them has already sat down in the seat closest to the dance floor?
1/4
Practice makes perfect
We know that four friends are sitting at a table together at the prom. We want to find the probability that a particular one of them will sit in the chair closest to the dance floor. Since the people are sitting at a table with a fixed reference point, this is a linear permutation. Therefore, there are 4! ways in which the people can be seated, which is the number of all possible outcomes.
Number of All Possible Outcomes = 4!
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Number of All Possible Outcomes = 24To find the number of ways in which the people can be seated so that a particular one of them will sit in the chair closest to the dance floor, let's imagine a situation where this person is already sitting down. The 3 remaining people can be seated in 3! ways. Therefore, the number of favorable outcomes in our situation is 3!.
Number of Favorable Outcomes = 3!
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Number of Favorable Outcomes = 6
The probability that a particular person will sit in the chair closest to the dance floor is the number of favorable outcomes divided by the number of all possible outcomes. Let's call our probability P(A).
P(A) = Number of Favorable Outcomes/Number of All Possible Outcomes
