Final answer:
A quality control inspector can select 8 out of 24 calculators in a certain number of ways, which is determined by using the combination formula C(n, k) = n! / [k!(n - k)!].
Step-by-step explanation:
To determine how many ways a quality control inspector randomly selects 8 calculators to inspect from 24 calculators, the concept of combinations is used. In this case, since the order of selection does not matter, the combination formula C(n, k) = n! / [k!(n - k)!] is applied, where 'n' is the total number of items to choose from, 'k' is the number of items to select, 'n!' is the factorial of 'n', and 'k!' is the factorial of 'k'.
In this scenario, 'n' is 24 (the total number of calculators) and 'k' is 8 (the number of calculators the inspector selects). Plugging these values into the formula, we get C(24, 8) = 24! / [8!(24 - 8)!] = 24! / (8! * 16!). Simplifying this gives us the number of ways to make the selection.
By performing the calculations, we obtain the result which is the number of different combinations the inspector can make when selecting 8 out of 24 calculators.