GATE Electrical 2017 Set 1 | GA | Question: 9

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?

• A. $21$
• B. $18$
• C. $16$
• D. $14$

Answer 1

Total ways to distribute 4 distinct shirts among 4 people = 4! = 24

Let
A = Arun gets Red
S = Shweta gets White

Ways Arun gets Red = 3! = 6
Ways Shweta gets White = 3! = 6
Ways both happen = 2! = 2

Using inclusion–exclusion:
Bad ways = 6 + 6 − 2 = 10

Valid ways = 24 − 10 = 14

Answer = 14