How many paths are there from point (0,0) to point (50,50) on the two-dimensional plane if each step along a path increments one coordinate and leaves the others unchanged and there is an impassable obstacle at the points (10,11) and (20, 19)? Provide a formula representation of your result that includes binomial coefficients, and navigate the reader through the development of your formula.

At bedtime, you read three books to your kids, Walker, Michael, and Luke. Together, they have 32 books. If you decide to randomly choose three books, what is the probability that the three you choose will consist of each of their favorite books? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

A license plate is to consist of two letters followed by four digits. Find the number of license plates possible if the first letter cannot be Z, and repetition is permitted.

A survey shows that 3 out of 4 of those drink coffee in a town with a population is 7900 adults how many of these adults would you expect to drink coffee?