In a class of 36 student 25 study chemistry 22 study mathematics and 25 study physics .17 study physics and mathematics, 18 study physics and chemistry and 15 study at least one of the three subject ,find
a) The number of student who study only mathematics and chemistry
To start this problem, we can use the principle of inclusion-exclusion. This states that:
Total number of students = number of students who study chemistry + number of students who study mathematics + number of students who study physics - number of students who study both chemistry and mathematics - number of students who study both physics and mathematics - number of students who study both chemistry and physics + number of students who study all three subjects.
Using this formula, we have:
Total number of students = 25 + 22 + 25 - 17 - 18 - 18 + 15
Total number of students = 54
Now, to find the number of students who study only mathematics and chemistry, we need to subtract the students who study other subjects or multiple subjects from the total number of students who study mathematics and chemistry.
Number of students who study only mathematics and chemistry = Total number of students who study mathematics and chemistry - (number of students who study all three subjects + number of students who study physics and chemistry + number of students who study physics and mathematics)
Number of students who study only mathematics and chemistry = 17 - (15 + 18 + 17)
Number of students who study only mathematics and chemistry = 17 - 50
Number of students who study only mathematics and chemistry = -33
This result is not possible as there cannot be negative number of students. Therefore, there must be no students who study only mathematics and chemistry.
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To find the number of students who study only mathematics and chemistry, we need to subtract the number of students who study all three subjects (physics, mathematics, and chemistry) from the number of students who study both mathematics and chemistry.
Given:
- Total number of students in the class: 36
- Number of students studying chemistry: 25
- Number of students studying mathematics: 22
- Number of students studying physics: 25
- Number of students studying physics and mathematics: 17
- Number of students studying physics and chemistry: 18
- Number of students studying at least one of the three subjects: 15
First, let's find the number of students who study all three subjects:
Using the principle of inclusion-exclusion, we can calculate this by subtracting the number of students studying at least one subject from the total number of students.
Number of students studying all three subjects = Total number of students - Number of students studying at least one subject
Number of students studying all three subjects = 36 - 15
Number of students studying all three subjects = 21
Next, let's find the number of students who study both mathematics and chemistry:
Number of students studying both mathematics and chemistry = Number of students studying mathematics + Number of students studying chemistry - Number of students studying all three subjects
Number of students studying both mathematics and chemistry = 22 + 25 - 21
Number of students studying both mathematics and chemistry = 26
Finally, we can find the number of students who study only mathematics and chemistry:
Number of students studying only mathematics and chemistry = Number of students studying both mathematics and chemistry - Number of students studying all three subjects
Number of students studying only mathematics and chemistry = 26 - 21
Number of students studying only mathematics and chemistry = 5
Therefore, the number of students who study only mathematics and chemistry is 5.