Powers and Permutations (Intro to Combinatorics)

This is the name given to the set of mathematical tools used to find the sizes of large sets:

What does  $\Pi$  mean?

For any trial with "r" actions, each with "a_i " possible results, the Fundamental Counting Principle says the size of the resulting sample space, respective of order, is...   

A restaurant offers the choice of 4 drinks, 8 appetizers, 6 main courses and 5 desserts. If you choose one item from each category, how many possible meals do you have to choose from?

A quiz consists of six multiple-choice items, each with four answer choices. If you must answer every question, how many ways are there to fill out this quiz?

A fair coin is flipped eight times. What is the probability that all of the flips come up tails?

What does the n stand for in combinatoric formulas?

What does the r stand for in combinatoric formulas?

If a trial consists of repeated selections with replacement from a single set, then, if order is respected, the resulting sample space is called a....

If a trial consists of    $r$    repeated selections with replacement from a single set with   $n$  elements, then, respective of order, the resulting sample space has a size of...