We have different methods to calculate probabilities.
Lists may refer to listing the possible outcomes and counting the successful outcomes according to the event we are trying to calculate.
For example what is the probability of selecting a day of the week and it turns out to be a week day. We would list the days of the week (obtaining 7 possible outcomes) and then the successful outcomes would be the 5 week days. Then, the probability would be 5/7.
Binomialpdf and Binomialcdf refer to the probability density function and cumulative probability of the binomial distribution. The former, Binomialpdf, is useful for individual probabilities (like X = k for a binomial random variable X) and the other, Binomialcdf, when calculating cumulative probabilities like X > k.
nCr is useful when the probability calcualtion requires calculating combinations of elements. nCr represents the number of possible combinations of r elements from a set of n elements where the order does not matter.