GATE | GATE-CS-2017 (Set 1) | Question 10

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?
(A) 21
(B) 18
(C) 16
(D) 14


Answer: (D)

Explanation: Total number of Shirts = 4 , Total candidates =4

  • So total combination of possibilities = 4 X 4 = 16
  • No.of ways  ‘Arun chooses red’ + No.of ways Shwetha chooses white ‘=  2

Therefore, Answer is 16-2 = 14.

Alternative approach –
We can solve using inclusion-exclusion:

Total possibilities = 4! = 24

Number of ways ‘Arun chooses red’ or ‘Shwetha chooses white’ = (Number of ways ‘Arun chooses red) + (Number of ways ‘Shwetha chooses white) – (Number of ways ‘Arun chooses red’ and ‘Shwetha chooses white) = 6 + 6 − 2 = 10

Required answer = 24 − 10 = 14.

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