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Answer:
Step-by-step explanation:
From the question, we have the following condition:
We know that each student who hears the rumor tells it to a student picked at random from the dormitory (excluding, of course, himself/herself and the person from whom he/she heard the rumor)
The 3rd student can therefore tell the rumour to n-2 students but only n-3 will accept it.
Consequently, the 4th student must not tell the 1st and second students.
We can rewrite this to observe a pattern:
Hence, the probability that the rumor is told r times without coming back to a student who has already is:
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