Answer :
Final answer:
The student can select 15 questions out of 20 in 15504 ways. If exactly three of the first 5 questions must be answered, there are 4550 ways to select the remaining questions.
Explanation:
a) The number of ways the student can select 15 questions out of 20 is represented by the combination formula, which is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of questions and r is the number of questions to be selected. In this case, n = 20 and r = 15. So, C(20, 15) = 20! / (15!(20-15)!) = 15504 ways.
b) To select exactly three questions from the first five, we need to choose 3 questions out of the first 5 and 12 questions out of the remaining 15. This can be done by multiplying the number of ways to choose 3 questions from the first 5 (C(5, 3)) and the number of ways to choose 12 questions from the remaining 15 (C(15, 12)). So, C(5, 3) * C(15, 12) = 10 * 455 = 4550 ways.
Learn more about Selecting questions in an examination here:
https://brainly.com/question/33248376
