Solve the problem
A student is told to answer any 8 out of 10 questions on an exam. In how many different ways can he choose the 8 questions to answer?
To solve this problem, we can use combinations.
The student needs to choose 8 out of 10 questions to answer. So, we can use the combination formula:
C(n, r) = n! / (r! * (n - r)!)
Where C(n, r) represents the number of combinations of choosing r items from a set of n items.
Applying this formula to our problem, we have:
C(10, 8) = 10! / (8! * (10 - 8)!)
= 10! / (8! * 2!)
Simplifying this expression, we have:
10! = 10 * 9 * 8! = 10 * 9 = 90
2! = 2 * 1 = 2
C(10, 8) = 10 * 9 / 2 = 45
Therefore, there are 45 different ways the student can choose the 8 questions to answer.