You can answer any 8 questions from the 12 questions on an exam. In how many different ways can you choose the 8 questions, assuming that the order in which you choose the questions is irrelevant?
you must use combination formula.
n!/r!(n-r)!
Sub values
12!/ 4! 8!
! is factorial.
Yes
a student answers 75% on a math exam correct. If he answer 60 questions correctly How many questions are on the exam.
To solve this problem, we can use the concept of combinations. Since the order in which we choose the questions is irrelevant, we need to find the number of ways to choose a subset of 8 questions from the total 12 questions.
The formula to calculate the combination is:
C(n, r) = n! / (r!(n - r)!)
Where n is the total number of items, r is the number of items we want to choose, and ! denotes factorial (the product of all positive integers less than or equal to a given number).
In this case, n = 12 (total questions) and r = 8 (questions to be chosen). Plugging these values into the formula, we get:
C(12, 8) = 12! / (8!(12 - 8)!) = 12! / (8!4!)
Calculating the factorial values:
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
4! = 4 x 3 x 2 x 1
Now, substituting these values back into the formula:
C(12, 8) = (12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / ((8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)(4 x 3 x 2 x 1))
Calculating this expression will give us the number of ways to choose 8 questions from a total of 12, considering the order is irrelevant.