Nine students - $3$ from Mr. Boes' class, $3$ from Mrs. Coes' class, and $3$ from Ms. Doe's class - have bought a block of 9 seats in a row for their schools homecoming game. If the seats are randomly assigned, what is the probability that students from each class will sit together in a block of 3 consecutive seats?
Students in class
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combinatorics
1 Answers
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There is a total of $9!$ possible arrangement if the students were to sit at random. If the students from each class are to sit together, the students from Mr. Boes' class can be arranged in $3!$ different ways, as will the students from Mrs. Coes' and Ms. Doe's class. The order in which the groups of each class can be arranged is also $3!$. So there is a total of $3!\cdot 3! \cdot 3! \cdot 3!$ arrangements for the classmates to sit together. Then the chance of that happening will be $\frac{3!\cdot 3! \cdot 3! \cdot 3!}{9!}$.