To determine the number of tests required for every possible pairing of three wires out of nine, we use combinations. The calculation is 9C3, which equals 84 tests needed.
The question requires us to determine the number of tests needed for every possible pairing of three wires out of nine. This problem can be solved using combinatorics, specifically by calculating combinations. A combination is a way of selecting items from a collection, such that the order of selection does not matter. In mathematical terms, the number of ways to choose k items from a set of n items is denoted by nCk (also written as C(n, k) or n choose k), which is calculated as n! / (k!*(n-k)!), where ! denotes factorial.
For this particular problem, we want to find the number of ways we can choose 3 wires from 9, which is 9C3. This calculation is performed as follows:
9C3 = 9! / (3!*(9-3)!)
9C3 = 9! / (3!*6!)
9C3 = (9*8*7) / (3*2*1)
9C3 = 84
Therefore, 84 different tests are required for every possible pairing of three wires out of nine.