Final answer:
The evaluation of C(120, 18) requires the use of the binomial coefficient formula. However, the correct value for C(120, 18) is not listed among the given answer choices, as it is a much larger number that requires computational tools to calculate.
Step-by-step explanation:
The question relates to evaluating the binomial coefficient C(120, 18), which represents the number of combinations of 120 items taken 18 at a time. This is a calculation used in combinatorics, a branch of mathematics. To evaluate this combination, it's necessary to use the binomial coefficient formula: C(n, k) = n! / (k!(n-k)!), where n! (n factorial) is the product of all positive integers up to n, and k! and (n-k)! are defined similarly. For very large values such as these, it's routinely done using a computer or a scientific calculator because manual calculation would be impractical and time-consuming. The answer choices given (A. 2, B. 380, C. 190, D. 210) suggest this question might be from a multiple-choice test, and the correct option for C(120, 18) is not among them, since the actual result of C(120, 18) is a much larger number.