Final answer:
The number of ways an examiner can assign 30 marks to 8 questions, giving not less than 2 marks in any question, is 21 C 7. So the correct answer is Option A.
Step-by-step explanation:
The question is asking for the number of ways an examiner can assign 30 marks to 8 questions, while ensuring that each question receives at least 2 marks. We can solve this using combinations. We can think of each question as a box, and we need to distribute the remaining marks (30 - 8*2 = 14) among these boxes in a way that no box receives more than 14 marks. Since each box must receive at least 2 marks, we subtract 16 marks (2*8) from the total marks. So, we need to distribute the remaining 14 marks among 8 boxes, which can be done using combinations as 14+8-1 C 8-1, which is equal to 21 C 7.
Therefore, the number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks in any question, is 21 C 7.
Hence, the correct option is A) ²⁰C₇.