Question

In a renowned software development company of 240 computer programmers 102 employees are proficient in Java, 86 in C#, 126 in Python, 41 in C# and Java, 37 in Java and Python, 23 in C# and Python, and just 10 programmers are proficient in all three languages. How many computer programmers are there those are not proficient in any of these three languages?

(a) 138

(b) 17

(c) 65

(d) 49

I had been asked this question in an internship interview.

This interesting question is from Discrete Probability in chapter Discrete Probability of Discrete Mathematics

Answer 1

Right answer is (b) 17

For explanation: Let U denote the set of all employed computer programmers and let J, C and P denote the set of programmers proficient in Java, C# and Python, respectively. So,  |U| = 240, |J| = 102, |C| = 86, |P| = 126, |J ∩ C| = 41, |J ∩ P| = 37, |C ∩ P| = 23 and |J ∩ C ∩ P| = 10. The number of computer programmers that are not proficient in any of these three languages is said to be same as the cardinality of the complement of the set J ∪ C ∪ P. First, we have to calculate |J ∪ C ∪ P| = 102 + 86 + 126 – 41 – 37 – 23 + 10 = 223. Now calculate |(J ∪ C ∪ P)’ | = |U| – |J ∪ C ∪ P| = 240 – 223 = 17. 17 programmers are not proficient in any of the three languages.