Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four…
2017
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
Attempted by 35 students.
Show answer & explanation
Correct answer: D
Key idea: count all permutations of distinct shirts and exclude assignments that violate dislikes using inclusion–exclusion.
Total assignments without restrictions: 4! = 24.
Assignments where Arun gets red: fix Arun = red, remaining 3 people can be assigned the remaining 3 shirts in 3! = 6 ways.
Assignments where Shweta gets white: similarly 3! = 6 ways.
Assignments where Arun gets red AND Shweta gets white: fix both, remaining 2 people arrange remaining 2 shirts in 2! = 2 ways.
Apply inclusion–exclusion: valid assignments = 24 - 6 - 6 + 2 = 14.
Answer: 14