Final answer:
The number of ways in which an examiner can assign 30 marks to 8 questions, with each question getting at least 2 marks, is calculated using the stars and bars method. After setting aside 2 marks per question, there are 14 marks left to distribute freely among the questions, leading to the combinatorial calculation of ^21C_7.
Step-by-step explanation:
The question asks about the number of ways an examiner can assign a total of 30 marks to 8 questions, ensuring that no question is awarded fewer than 2 marks. To solve this problem, we can use combinatorics principles. Since every question must get at least 2 marks, we start by allocating 2 marks to each of the 8 questions which accounts for 16 marks. We now have 30 - 16 = 14 marks to distribute among the 8 questions without any restrictions.
Using the stars and bars method (also known as balls and urns), we imagine the 14 marks are stars and we need to place 7 bars to divide them into 8 sections (for the 8 questions). The number of ways to arrange these stars and bars is the same as choosing 7 positions out of the total 14 + 7 positions available, which is 21 choose 7 or ^21C_7.
Therefore, the answer is option A. ^21C_7.