In a class, there are n students including the students P and Q. What is the probability that P and Q sit together if seats are assigned randomly?
- A. \frac{1}{n}
- B. \frac{2}{n} ✓
- C. \frac{4}{n}
- D. \frac{1}{2n}
Correct Answer: B. \frac{2}{n}
Explanation
The total number of ways to arrange n students is n!. If P and Q sit together, treat them as a single unit. The number of arrangements of this unit and the remaining (n-2) students is (n-1)!. P and Q can swap positions in 2! = 2 ways. The favorable arrangements are 2 \cdot (n-1)!. The probability is \frac{2(n-1)!}{n!} = \frac{2}{n}.
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