In a class of 40 student, a student can study french or history or both , if 20 study french , 23 study history and 7 study neither . How many students study both subject
If x study both, then
20+23 - x = 40 - 7
To find out how many students study both subjects, we need to use the principle of inclusion-exclusion.
Let's denote the number of students studying French as F, the number of students studying History as H, and the number of students studying both subjects as B.
From the given information, we know that F = 20 (20 students study French) and H = 23 (23 students study History).
We are also given that there are 7 students who study neither subject.
Using the principle of inclusion-exclusion, the total number of students in the class can be calculated as follows:
Total Students = F + H - B + Neither
Total Students = 20 + 23 - B + 7
Since we know that the total number of students in the class is 40, we can write the equation as:
40 = 20 + 23 - B + 7
Simplifying the equation:
40 = 50 - B
Rearranging the equation to isolate B:
B = 50 - 40
B = 10
Therefore, 10 students study both French and History.