70 students are studying mathematics,physics & chemistry.40 students study mathematics,35 study physics and 30 study chemistry.15 students are studying all the three subjects.How many students are studying exactly two of the subjects
If there are a,b,c students studying exactly two of the subjects, taken in pairs, then
(40+35+30)-(a+15 + b+15 + c+15)+15 = 70
a+b+c = 5
So, 5 students are taking exactly two of the subjects.
In a class of 120 students each student studies at least one of the subjects from history English & maths 59 study history 67 study English & 73 study maths. 34 study maths & history, 26 english & maths & 33 history & english
How many students study exactly two subjects.?
Well, it seems like these students don't want to miss out on any subject! To find the number of students studying exactly two subjects, let's do a little math.
First, let's add up the number of students studying each subject: 40 students study mathematics, 35 study physics, and 30 study chemistry. However, if we add these numbers, we will be double-counting the 15 students who are studying all three subjects.
To avoid double-counting, let's subtract the number of students studying all three subjects from the total. So, 40 + 35 + 30 - 15 equals 90.
Therefore, there are 90 students studying exactly two subjects. These students must be really eager to expand their knowledge in multiple areas!
To find the number of students studying exactly two of the subjects, we need to calculate the total number of students who are studying mathematics and physics, mathematics and chemistry, and physics and chemistry. Then we will subtract the students who are studying all three subjects to get the final answer.
Let's break it down step by step:
1. The number of students studying mathematics and physics can be found by adding the number of students studying mathematics (40) and the number of students studying physics (35). So, 40 + 35 = 75 students are studying mathematics and physics.
2. The number of students studying mathematics and chemistry can be found by adding the number of students studying mathematics (40) and the number of students studying chemistry (30). So, 40 + 30 = 70 students are studying mathematics and chemistry.
3. The number of students studying physics and chemistry can be found by adding the number of students studying physics (35) and the number of students studying chemistry (30). So, 35 + 30 = 65 students are studying physics and chemistry.
Now, let's calculate the number of students studying exactly two subjects:
Step 4: Add the number of students studying mathematics and physics (75), mathematics and chemistry (70), and physics and chemistry (65). 75 + 70 + 65 = 210 students are studying either two or all three subjects.
Step 5: Subtract the number of students who are studying all three subjects (15) from the total calculated in step 4: 210 - 15 = 195 students are studying exactly two of the subjects.
Therefore, there are 195 students who are studying exactly two of the subjects.
(M+P+C)-(M&P+P&C+M&C)+All=70
=> M&P+P&C+M&C = 40+35+30-70
=> M&P+P&C+M&C = 50