I'm doing some preparations for an upcoming exam, and a little confused about this problem:
"In an airport, 70 flight landings per hour are allocated among 4 runways. Any flight can land on any of the runways and each flight lands on exactly one runway. The flight traffic controllers are only interested in the number of flights on each runway and not which flights they are.
How many ways can the flight traffic controller allocate the incoming 70 flights per hour to the runways? (Some runways may have no flights)"
In my understanding, in this problem, repetitions are not allowed, and order does not matter:
Repetitions are not allowed since once you put a plane down on one runway, you can't put that plane down on another runway.
Order does not matter because as the question states, "The flight traffic controllers are only interested in the number of flights on each runway, not which flights they are"
When we have repetitions not allowed and order doesn't matter, we use the Choose formula $C(n,r)$ which yields $C(70,4)$
However this is incorrect, the correct solution states:
The problem is equivalent to finding the total number of solutions to $x1 + x2 + x3 + x4 = 70$ which ends up being $C(73,3)$. Using the formula $C(r+n-1, n-1)$ which correspond to situations in which repetitions ARE allowed, and order doesn't matter.
What am I missing?