How to Calculate the Odds of Physical Attack Data Loss for a ZFS Array

Note: this method should be generalizable to other array and filesystem types. The general method is:

1. Calculate the number of data loss drive destruction combinations for a given number of destroyed drives
2. Calculate the number of non-data loss drive destruction combinations for a given number of destroyed drives
3. Sum the above
4. Divide 1) by 3)

Problem Statement

Consider a ZFS array with a given redundancy level, x. Assume a physical attacker with no knowledge of the array's configuration destroys x + 1 (the minimum number of destroyed drives necessary to result in data loss) drives. What is the probability that said destruction actually results in data loss?

Background

It is possible for a ZFS array to lose more than x + 1 drives without suffering data loss. Consider, for example, an array containing 2 x 4 HDD RAIDZ2 vdevs. The redundancy is given by the "2", meaning that each vdev can lose 2 HDDs without suffering data loss. If either vdev loses 3 or more HDDs, though, the array suffers data loss. Ergo, x + 1, in this case is 3.

However, what if both vdevs lose 2 HDDs each, for a total of 4 HDDs? Because neither vdev has exceeded its redundancy, neither would suffer data loss.

Solution Method

Clearly, the aforesaid is a probability problem. What might not be immediately obvious, though, is that it's also a combinations problem. For a quick primer on this,