Q: In a survey of a group of 100 computing students, it was found that 32 knew Java, 33 knew C, 32 knew Python, 5 knew both Java and C, 7 knew both C and Python while none of the students knew both Java and Python. How many students knew none of the three languages?
Attempt:
First attempt was I guessed 3 because it only adds up to 97 so I assumed 3 students knew none of them.
Then I tried it out and got 27 for java, 21 for C and 25 for python, added those up and got 72. Minus 72 from 100 and got 28 as my final answer for students who know none.
My teacher has no marking scheme for this question, this is a practice q. Anyone know the solution?
Since no student knows both Java and Python, no student knows all three. Inclusion/exclusion then gives the number of students knowing at least one of the languages as $$32+33+32-5-7-0+0=85$$ Subtracting from $100$ gives $15$ students not knowing any language.