a.) Suppose that n people are seated in a random manner in a row of n...
a.) Suppose that n people are seated in a random manner in a row of n theater seats. What is the probability that two particular people A and B will be seated next to each other?
The answer to the question is 2/n, but I'm not sure how to do the process. My teacher said that it was the # of favorable outcomes/ total number of outcomes, which was 2* (n-1)! / n!, which simplifies to 2/n. Is this process using combinations or permuations?
b.) If k people are seated in a random manner in a row containing n seats (n > k), what is the probability that the people will occupy k adjacent seats in the row?
The answer was n-k+1 / (n! / (n-k)! k!) ). Can you explain why the numerator is n-k+1 instead of something with a factorial like (n-k+1)! like the first question? Is it using permutations instead of combinations?
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