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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. $14$
in Numerical Ability by Veteran (431k points)
edited by | 4.4k views

5 Answers

+41 votes
Best answer
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: $D$
by Active (1.4k points)
edited by
+1
nice one..
0
Why you subtracted 2 in 6+6-2.

My point is if A got red and S got white ,it should also removed from 4!.

Please reply!!
0

Please review it 


0
Nice explanation
+1
Why can't it be 3 x 4 x 4 x 3 = 144 ?

Question doesn't say that two or more person can't have same colored shirts.

Aren't the options given wrong?
+3

see the question again - "pile of four shirts" .i.e, there are only four shirts to choose from.

 

+23 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
by Active (2.3k points)
+13 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.
by Boss (13.7k points)
+11 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 )
by Active (1.1k points)
0 votes

Simplest Approach 

by Junior (923 points)
Answer:

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