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In how many ways can 6 apples be distributed among 3 boys, there being no restriction to the number of, apples each boy may get?
- a)729
- b)739
- c)759
- d)749
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In how many ways can 6 apples be distributed among 3 boys, there being...
Each apple can be given to anyone of the 3 boys and this can be done in 3 ways. ∴ The required number of ways =36=729
Most Upvoted Answer
In how many ways can 6 apples be distributed among 3 boys, there being...
Distribution of 6 apples among 3 boys with no restriction on the number of apples each boy may get can be solved using the concept of stars and bars or balls and urns.
Stars and Bars:
In this method, we imagine the apples as stars and the dividers between the boys as bars. The idea is to distribute the stars (apples) among the bars (boys). The number of ways to distribute the apples is equal to the number of ways to arrange the stars and bars.
Step 1: Represent the distribution using stars and bars:
***|*|*
The above representation indicates that the first boy gets 3 apples, the second boy gets 1 apple, and the third boy gets 2 apples.
Step 2: Determine the number of ways to arrange the stars and bars:
In this case, we have a total of 6 apples and 3 boys. So, we need to arrange 6 stars and 3-1 = 2 bars. The number of ways to arrange them is given by the formula:
(number of stars + number of bars) choose (number of bars)
= (6 + 2) choose 2
= 8 choose 2
= 8! / (2! * (8-2)!)
= 8! / (2! * 6!)
= (8 * 7 * 6!)/ (2 * 1 * 6!)
= (8 * 7) / (2 * 1)
= 56 / 2
= 28
Therefore, the number of ways to distribute 6 apples among 3 boys with no restrictions is 28.
Hence, the correct answer is option A) 729, which is incorrect.
Stars and Bars:
In this method, we imagine the apples as stars and the dividers between the boys as bars. The idea is to distribute the stars (apples) among the bars (boys). The number of ways to distribute the apples is equal to the number of ways to arrange the stars and bars.
Step 1: Represent the distribution using stars and bars:
***|*|*
The above representation indicates that the first boy gets 3 apples, the second boy gets 1 apple, and the third boy gets 2 apples.
Step 2: Determine the number of ways to arrange the stars and bars:
In this case, we have a total of 6 apples and 3 boys. So, we need to arrange 6 stars and 3-1 = 2 bars. The number of ways to arrange them is given by the formula:
(number of stars + number of bars) choose (number of bars)
= (6 + 2) choose 2
= 8 choose 2
= 8! / (2! * (8-2)!)
= 8! / (2! * 6!)
= (8 * 7 * 6!)/ (2 * 1 * 6!)
= (8 * 7) / (2 * 1)
= 56 / 2
= 28
Therefore, the number of ways to distribute 6 apples among 3 boys with no restrictions is 28.
Hence, the correct answer is option A) 729, which is incorrect.
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In how many ways can 6 apples be distributed among 3 boys, there being no restriction to the number of, apples each boy may get?a)729b)739c)759d)749Correct answer is option 'A'. Can you explain this answer? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about In how many ways can 6 apples be distributed among 3 boys, there being no restriction to the number of, apples each boy may get?a)729b)739c)759d)749Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways can 6 apples be distributed among 3 boys, there being no restriction to the number of, apples each boy may get?a)729b)739c)759d)749Correct answer is option 'A'. Can you explain this answer?.
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