Final answer:
The number of ways to assign 30 marks to 8 questions, with each question receiving at least 2 marks, can be solved using 'stars and bars' combinatorics. The correct calculation is (21 choose 7), but the options provided in the question do not correspond to this combinatorial number. The question might contain a mistake in the options provided.
Step-by-step explanation:
The question asks us to find the number of ways an examiner can assign 30 marks to 8 questions, subject to the constraint that no question receives less than 2 marks. This is a problem in the field of combinatorics, a branch of Mathematics that deals with counting, arrangement, and combination of objects.
Since each question must have at least 2 marks, we first allocate 2 marks per question, using up 16 marks. We are left with 30 - 16 = 14 marks to distribute among the 8 questions. This problem can be visualized as the distribution of 14 indistinguishable objects (marks) into 8 distinguishable bins (questions), which allows for empty bins since each question already has its minimum of 2 marks.
The solution uses a combinatorial method known as 'stars and bars'. Here, we need to determine the number of ways to insert 7 dividers among 14 stars (where stars represent marks and dividers represent the separation between the marks allocated to different questions).
There are (14 + 7) choose 7, which is (21 choose 7), different ways to complete this task. However, the options provided in the question seem incorrect as they suggest fractions, which are not suitable in the context of combinatorial counting.
Therefore answer is A. (21/7).