GATE EE 2017 Set 1 — Question 64
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General Aptitude → Quantitative Aptitude → Permutations & Combinations
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Question
Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white. Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes?
Correct answer
(D) 14
Solution
Total number of ways to distribute 4 distinct shirts among 4 people is .
Let be the set of ways where Arun gets the red shirt. .
Let be the set of ways where Shweta gets the white shirt. .
The intersection is the set of ways where Arun gets red AND Shweta gets white. .
By the Principle of Inclusion-Exclusion, the number of ways where at least one person gets a shirt they dislike is .
The number of valid ways where no one gets a shirt they dislike is .
Let be the set of ways where Arun gets the red shirt. .
Let be the set of ways where Shweta gets the white shirt. .
The intersection is the set of ways where Arun gets red AND Shweta gets white. .
By the Principle of Inclusion-Exclusion, the number of ways where at least one person gets a shirt they dislike is .
The number of valid ways where no one gets a shirt they dislike is .
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