Final answer:
The word 'Combinatorics' will generate more anagrams than 'Combinatorica' because it has one additional distinct letter, which is the 's'. With the extra letter, there are more permutations possible for 'Combinatorics'. It is a mathematical problem that applies combinatorial analysis to determine the number of anagrams.
Step-by-step explanation:
The question asks which word, "Combinatorics" or "Combinatorica", gives rise to more anagrams. Anagrams are a rearrangement of all the letters in a word to form a new word. When comparing the number of anagrams Combinatorics and Combinatorica can generate, we need to consider the number of distinct letters in each word and their frequency. The two words in question are almost identical except that "Combinatorics" has an additional 's'.
To determine the number of anagrams, we use the formula for permutations of multiset which is given by dividing the factorial of the number of elements by the product of the factorials of the frequency of each element. Since "Combinatorica" is missing the 's' that "Combinatorics" has, it has one less distinct character and thus will have fewer arrangements. So, Combinatorics will have more anagrams because the additional 's' increases the number of possible permutations.
The correct answer is (a) Combinatorics. This is a problem in the discipline of combinatorics, a branch of mathematics concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It's also a practical exercise in systematic problem-solving and applying mathematical principles to real-world problems.