A final examination requires that a student answer any 4 out of 6 questions. In how many ways can this be done?
Answer Details
To calculate the number of ways a student can answer any 4 out of 6 questions, we can use the combination formula, which is:
nCk = n! / (k! * (n-k)!)
where n is the total number of items, k is the number of items to be selected, and ! represents the factorial function.
In this case, we have n = 6 (the total number of questions on the exam) and k = 4 (the number of questions the student must answer). So we can calculate the number of ways to select 4 questions out of 6 using the combination formula as follows:
6C4 = 6! / (4! * (6-4)!) = (6 * 5 * 4 * 3) / (4 * 3 * 2 * 1) = 15
Therefore, the answer is 15, which means that a student can answer any 4 out of 6 questions in 15 different ways.