Out of all stations only 1 allowed to transmit so to select 1 station out of N stations there are N ways possible (nC1 ) then
it must transmit and other n-1 stations should not transmit
therefore n * p * (1-p)*(1-p)*.............(1-p)
Event 1: Only one station should transmit
We can select one station out of 1 station in C(n,1 ) ways = n
This station has to transmit with the probability 'p'
Therefore, P(E1) = n * p
Event 2: Remaining (n-1) stations should not transmit
Then remaining (n-1) stations should not transmit.
So, for all of them probability will be (1-P)
therefore, P(E2) = (1-p)^(n-1).
Now, both the events should occur simultaneously
Hence, n * p * (1 - p )^(n-1)