Clarification on the intended meaning of a probability problem I am just wondering if anyone can help with this question:

A radio station held a competition where contestants were invited to pick a number from $1$ to $50$. If a contestant picked the ‘winning’ number they won a trip to Vegas. The station picked a new ‘winning’ number at random each time a new contestant played the game. The radio station allowed ﬁve contestants to play every day over the course of one week.
  
  
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*Compute the probability that the station will have to pay out for exactly 
      one Vegas trip.
  

I know that there will be 35 people in total who will guess the number but can the 'winning' number be reused or is it without replacement?
 A: The only way this makes sense if it is with replacement. That is each contestant can chose any number.  Here is why: 


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*If it were without replacement it would not make sense to assign a new winning number after each try. This makes sense in a scenario with replacement so that each contestant still has a $1$ in $50$ chance of winning, as earlier attempts do not "eliminate" a number.

*Somewhat less seriously If it were without replacement and this is on radio it would not be easy to communicate which number are still available. 
The above are in my opinion fairly strong reasons for it being with replacement, but in an exam-situation I would still advise to ask for clarification. Now one never knows but I would hope you do get a reply to a to the point question on the interpretation of the question. Do not say something vague like "I do not understand this." but ask specifically like this: "It is not clear to me from the text, can a participant chose the same number as a preceding participant. Which scenario is to be assumed?"
