I have a doubt reagarding some questions from the week 16 quiz.

Please see this question about transmitting bits. This was the solution given:

My doubt is … why aren’t we including the combination term in the probabilities? I mean why aren’t we multiplying 10C3 in P(X=3) ?

and similarly, here, in another problem,

why aren’t we multiplying 20C19 in P(X=19) ?

Please reply.