in a class of 50 students, 17 are not intelligent, 15 are hard working and 11 are neither hardworking nor intelligent. A student will pass if and only if the student is both intelligent and hardworking. how many of this class will fail.

Answer 1

We can start solving this problem by using the principle of inclusion-exclusion.

Total number of students = 50
Number of students not intelligent = 17
Number of students hardworking = 15
Number of students neither hardworking nor intelligent = 11

Let's first find the total number of students who are both intelligent and hardworking. We can do this by subtracting the number of students who are not intelligent or not hardworking or both from the total number of students:

Total number of students who are both intelligent and hardworking = 50 - 17 - 15 + 11
= 29

So, there are 29 students who will pass.

To find the number of students who will fail, we need to subtract the number of students who will pass from the total number of students:

Number of students who will fail = 50 - 29
= 21

Therefore, 21 students will fail.