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39 votes
39 votes

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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6 Answers

Best answer
59 votes
59 votes
Total possibilities $=4! = 24.$

No. of ways  'Arun chooses red' or 'Shwetha chooses white'

$=\text{(no.of ways  `Arun chooses red')}$
$+ \text{(no.of ways  `Shwetha chooses white')}$
$-(\text{no.of ways  `Arun chooses red' and `Shwetha chooses white')}$

$=6+6-2 = 10$

required $=24-10=14.$

Correct Answer: $D$
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34 votes
34 votes
Ans will be D) 14

case 1 if Arun takes  pink then shweta can take either red or blue (so 2 choices) and gulab or neel have 2 and 1 choice respectively

so total ways in this case =2x2x1=4

Case 2

if Arun takes  blue then shweta can take either red or pink (so 2 choices) and gulab or neel have 2 and 1 choice respectively

so total ways in this case =2x2x1=4

Case 3

if Arun takes  white  then shweta can take either red or pink or blue (so 3 choices) and gulab or neel have 2 and 1 choice respectively

so total ways in this case =3x2x1=6

total  =4+4+6 =14 cases
22 votes
22 votes
3p1 +4p1+4p1+3p1=14( as gulaab and neel can select any color of shirt  while arun and shweta can have only 3 shirt to choose )
20 votes
20 votes
Another ways is  

(1) When Arun takes white color then  1*3*2*1 (Arun *  Gulab *  Neel * Shweta) = 6

(2) When Arun does not takes white color then 2*1*2*2 (Arun *  Gulab *  Neel * Shweta) = 8

So Total is 8+6 = 14. Answer is (D) Part.
Answer:

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