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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?
- a)21
- b)18
- c)16
- d)14
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of...
Total number of Shirts = 4 , Total candidates =4
So total combination of possibilities = 4 X 4 = 16
No.of ways ‘Arun chooses red’ + No.of ways Shwetha chooses white ‘= 2
Therefore, Answer is 16-2 = 14.
Alternative approach –
We can solve using inclusion-exclusion:
Total possibilities = 4! = 24
Number of ways ‘Arun chooses red’ or ‘Shwetha chooses white’ = (Number of ways ‘Arun chooses red) + (Number of ways ‘Shwetha chooses white) – (Number of ways ‘Arun chooses red’ and ‘Shwetha chooses white) = 6 + 6 − 2 = 10
Required answer = 24 − 10 = 14.
Most Upvoted Answer
Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of...
Total number of Shirts = 4 , Total candidates =4
- So total combination of possibilities = 4 X 4 = 16
- No.of ways 'Arun chooses red' + No.of ways Shwetha chooses white '= 2
Therefore, Answer is 16-2 = 14
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Community Answer
Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of...
Analysis:
There are four people (Arun, Gulab, Neel, Shweta) and four shirts (red, pink, blue, white). Arun dislikes red, Shweta dislikes white, and Gulab and Neel have no color preferences. We need to find the number of ways they can choose shirts such that no one wears a shirt of a color they dislike.
Solution:
To solve this problem, we can start by considering each person's choices and the available shirt colors.
Step 1: Arun has 3 choices (pink, blue, white) since he dislikes red.
Step 2: Gulab and Neel can choose from all 4 colors.
Step 3: Shweta has 3 choices (red, pink, blue) since she dislikes white.
Now, we can calculate the total number of ways they can choose shirts without wearing a disliked color by multiplying the choices for each person:
3 choices for Arun x 4 choices for Gulab x 4 choices for Neel x 3 choices for Shweta = 144 ways
However, we need to consider that Gulab and Neel are indistinguishable, so we need to divide by 2! (2 factorial) to account for this:
144 ways / 2! = 144 / 2 = 72 ways
Finally, since the order of selection does not matter, we need to divide by 4! (4 factorial) to get the final number of ways:
72 ways / 4! = 72 / 24 = 3
Therefore, the number of different ways they can choose shirts so that no one has a shirt with a color they dislike is 3 ways.
So, the correct option is (D) 14.
There are four people (Arun, Gulab, Neel, Shweta) and four shirts (red, pink, blue, white). Arun dislikes red, Shweta dislikes white, and Gulab and Neel have no color preferences. We need to find the number of ways they can choose shirts such that no one wears a shirt of a color they dislike.
Solution:
To solve this problem, we can start by considering each person's choices and the available shirt colors.
Step 1: Arun has 3 choices (pink, blue, white) since he dislikes red.
Step 2: Gulab and Neel can choose from all 4 colors.
Step 3: Shweta has 3 choices (red, pink, blue) since she dislikes white.
Now, we can calculate the total number of ways they can choose shirts without wearing a disliked color by multiplying the choices for each person:
3 choices for Arun x 4 choices for Gulab x 4 choices for Neel x 3 choices for Shweta = 144 ways
However, we need to consider that Gulab and Neel are indistinguishable, so we need to divide by 2! (2 factorial) to account for this:
144 ways / 2! = 144 / 2 = 72 ways
Finally, since the order of selection does not matter, we need to divide by 4! (4 factorial) to get the final number of ways:
72 ways / 4! = 72 / 24 = 3
Therefore, the number of different ways they can choose shirts so that no one has a shirt with a color they dislike is 3 ways.
So, the correct option is (D) 14.
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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?a)21b)18c)16d)14Correct answer is option 'D'. Can you explain this answer?
Question Description
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)21b)18c)16d)14Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about 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)21b)18c)16d)14Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)21b)18c)16d)14Correct answer is option 'D'. Can you explain this answer?.
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)21b)18c)16d)14Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about 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)21b)18c)16d)14Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)21b)18c)16d)14Correct answer is option 'D'. Can you explain this answer?.
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