- #1

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## Homework Statement

A hostel is occupied by 40 tourists and a hostel-keeper. The hostel-keeper spreads a rumour to one of the tourists, who then tells it to another one, and so on.

1) Find the probability that the rumour is spreaded 15 times without returning to the hostel-keeper.

2) Find the probability that the rumour is spreaded 15 times without nobody hearing it twice

## The Attempt at a Solution

I'm a little stuck with this, because I don't know what kind of problem it is. For 1), am I suposed to think that the rumour can be heard more than once by the rest but not by the hostel keeper?

If so, then the |[tex]\Omega[/tex]| = 40

^{15}, because each person can hear it twice, three times, etc. But it wouldn't make sense that a rumour is heard 15 times by the same person, because that means that the tourists told the rumour to itself 15 times.

Then, otherwise, |[tex]\Omega[/tex]|= (40)

_{15}, that is 40!/25! But then nobody would hear it twice, because 40!/26! = 40*39*38*37*36*35*34*33*32*31*30*29*28*27*26, which is to say that the first person to hear the rumour can then tell it to 40 other people and the one to hear it can tell it to 38 other people (everybody else but itself and the person who told it to him/her, which forbids it to be shared twice with the same person).

So I don't even know how many events can happen. Point 2) only brings more confusion. Any thoughts?

Thanks.