Hotel overbooking task

#1
Hello together,

I am a bit lost with this problem that I need to answer for a university project and I hope someone is able to help me solving it.

The case is, that there is a hotel, and 5,5% of the reservations did not show up at the end.
We want to accept 49 reservations and the hotel has 47 rooms. With the given 5,5% „not show up“ rate on average 46,305 reservations will show up.

I need to find out, how high the probability is, that more than 47 reservations (out of 49) will show up so that the arriving customers exceed the number of rooms the hotel has.

Can anyone help me here or at least help me to find a way to calculate this? I don’t know if it helps, but the 5,5% not show up rate are based on 40 observations.

Thank you very much!
Stef