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GATE 2017 EE – Question 9

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 2 marks · Multiple choice

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?

  1. 21
  2. 18
  3. 16
  4. 14

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Correct answer: (D) 14

Explanation

All ways to give 4 shirts to 4 people is $4! = 24$. The ways where Arun gets red is $3! = 6$, and where Shweta gets white is also 6. Both together gives $2! = 2$. So the valid ways are $24 - 6 - 6 + 2 = 14$.