$18\mathrm{.}8-3.$ To help fill its seats for a particular flight, an airline offers a special nonrefundable fare of $$\backslash$$ $100$$ for customers who make a reservation at least $21$ days in advance and satisfy other restrictions. Thereafter, the fare will be $$\backslash$$ $300$$$.$ A total of $100$ reservations will be accepted. The number of customers who have requested a reservation at full fare for this flight in the past always has been at least $31$ and not more than $50.$ It is estimated that the integer numbers between $31$ and $50$ are equally likely.

Use the model for capacity$-$controlled discount fares to determine how many of the reservations should be reserved for customers who would pay full fare.