In a class of 300 students , they were given mathematics test in three subjects namely , Economics , Statistics and Mathematics , 90 students failed in Economics , 100 failed in Statistics , 96 failed in Mathematics , 60 failed in Economics and Statistics , 64 failed , in statistics and Mathematics , to failed in Economics and Mathematics while 50 failed in all subjects . Find number of students who failed in at least one subject .
To find the number of students who failed in at least one subject, we can use the principle of inclusion-exclusion.
Step 1: Find the number of students who failed in each subject individually:
- Number of students who failed in Economics = 90
- Number of students who failed in Statistics = 100
- Number of students who failed in Mathematics = 96
Step 2: Find the number of students who failed in the intersection of two subjects:
- Number of students who failed in Economics and Statistics = 60
- Number of students who failed in Statistics and Mathematics = 64
- Number of students who failed in Economics and Mathematics = To be determined
Step 3: Find the number of students who failed in the intersection of all three subjects:
- Number of students who failed in all three subjects = 50
Step 4: Calculate the number of students who failed in at least one subject using the principle of inclusion-exclusion:
- Number of students who failed in at least one subject = (Number of students who failed in Economics) + (Number of students who failed in Statistics) + (Number of students who failed in Mathematics) - (Number of students who failed in Economics and Statistics) - (Number of students who failed in Statistics and Mathematics) - (Number of students who failed in Economics and Mathematics) + (Number of students who failed in all three subjects)
Based on the given information and principle of inclusion-exclusion, we have:
- Number of students who failed in at least one subject = 90 + 100 + 96 - 60 - 64 - (Number of students who failed in Economics and Mathematics) + 50
To solve for the unknown value, we can rearrange the equation:
- Number of students who failed in Economics and Mathematics = 90 + 100 + 96 - 60 - 64 + 50 - (Number of students who failed in at least one subject)
Therefore, to find the number of students who failed in at least one subject, we need the value of (Number of students who failed in Economics and Mathematics).