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When dealing with permutations, we are interested in all possible ways to arrange a set of items. If you have a set of 8 different statistics exams, the number of ways to arrange them in order is found using permutations.

Permutations consider the sequence in which elements appear. For example, the arrangement ABCD is different from BACD, although they use the same elements. That's why, when calculating permutations, every distinct arrangement counts. In permutations, order matters and each unique order is considered separately.

The total number of permutations of 8 distinct items is calculated using the factorial operation. This is represented by 8! (8 factorial), which tells us how many ways we can arrange these 8 exams.

The factorial operation is crucial for finding permutations. The symbol '!' denotes factorial, and it means multiplying a series of descending natural numbers. For example, factorial 8 (written as 8!) is calculated by multiplying all whole numbers from 8 down to 1.

Mathematically, this looks like:
\[8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320\]

This means there are 40,320 different ways to arrange 8 exams. Each specific sequence (like grading in alphabetical order) is just one of these 40,320 ways.

Probability helps us measure how likely an event is to occur. To find the probability of grading exams in alphabetical order, we need to consider both the total number of possible arrangements and the number of favorable outcomes.

From the previous sections, we know that there are 40,320 possible ways to grade the 8 exams.

Now, the favorable outcome is grading the exams in exactly alphabetical order, which is unique. There is only one such order.

The probability P of a favorable event happening is calculated as:
\[P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}}\]

Applying this to our problem:
\[P(\text{Alphabetical Order}) = \frac{1}{8!} = \frac{1}{40320}\]

So, the probability of grading all exams in alphabetical order by the students' names is \[ \frac{1}{40320}.\]