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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. $14$

edited | 4.4k views

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
+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!.

0

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.

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)
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)
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)

Simplest Approach

by Junior (923 points)