The reason why you can't use the binomial formula here is that it only works if the probability of each event is constant. That's not the case here....
Your link is locked behind a registration wall. Can you please upload the image to this forum, so that I (and other helpers) do not need to register...
Often times when I'm stuck on a math problem, I find it immensely helpful to consider a smaller/simpler version of the problem, to help me get a feel...
Truthfully, I'm not really sure what more you want in order to consider it a "professional" solution/explanation. The problem asks you to explain why...
What you've done so far is fine, and if you continue to simplify and evaluate the limit you will get the correct answer. But I think it would be way...
Actually, Denis, the problem text specifically instructed OP to "find x," directly implying that they were meant to come up with a numerical solution...