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Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3 .Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3 . [2011]
- a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- b)Statement-1 is true, Statement-2 is false.
- c)Statement-1 is false, Statement-2 is true.
- d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Statement-1: The number of ways of distributing 10 identical balls in ...
The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box empty is same as the number of ways of selecting (r – 1) places out of (n – 1) different places, that is n-1Cr -1 .
Hence required number of ways = 10-1C4-1 = 9C3
∴ Both statements are correct and second statement is a correct explanation of statement -1.
Hence required number of ways = 10-1C4-1 = 9C3
∴ Both statements are correct and second statement is a correct explanation of statement -1.
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Statement-1: The number of ways of distributing 10 identical balls in ...
Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3.
Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3.
To evaluate the validity of the given statements, let's analyze each statement individually:
Statement-1:
The number of ways to distribute 10 identical balls in 4 distinct boxes such that no box is empty can be calculated using the concept of stars and bars.
In this scenario, we can represent the 10 identical balls as 10 stars (**********) and represent the 4 distinct boxes using 3 bars (|||). The balls before the first bar go into the first box, the balls between the first and second bar go into the second box, and so on.
For example, if we have the arrangement **|***|****|**, it means the first box has 2 balls, the second box has 3 balls, the third box has 4 balls, and the fourth box is empty.
The number of ways to arrange the stars and bars can be calculated using the formula for combinations. We have a total of 10 stars and 3 bars to arrange, so the number of ways is given by 13C3, which is equal to 286.
Therefore, Statement-1 is true.
Statement-2:
The number of ways to choose any 3 places from 9 different places can also be calculated using the concept of combinations.
We have a total of 9 different places, and we want to choose 3 of them. The number of ways to do this is given by 9C3, which is equal to 84.
Therefore, Statement-2 is true.
Explanation:
Statement-2 is a correct explanation for Statement-1 because the number of ways to distribute 10 identical balls in 4 distinct boxes such that no box is empty (286) is equal to the number of ways to choose any 3 places from 9 different places (84).
Hence, the correct answer is option 'D'.
Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3.
To evaluate the validity of the given statements, let's analyze each statement individually:
Statement-1:
The number of ways to distribute 10 identical balls in 4 distinct boxes such that no box is empty can be calculated using the concept of stars and bars.
In this scenario, we can represent the 10 identical balls as 10 stars (**********) and represent the 4 distinct boxes using 3 bars (|||). The balls before the first bar go into the first box, the balls between the first and second bar go into the second box, and so on.
For example, if we have the arrangement **|***|****|**, it means the first box has 2 balls, the second box has 3 balls, the third box has 4 balls, and the fourth box is empty.
The number of ways to arrange the stars and bars can be calculated using the formula for combinations. We have a total of 10 stars and 3 bars to arrange, so the number of ways is given by 13C3, which is equal to 286.
Therefore, Statement-1 is true.
Statement-2:
The number of ways to choose any 3 places from 9 different places can also be calculated using the concept of combinations.
We have a total of 9 different places, and we want to choose 3 of them. The number of ways to do this is given by 9C3, which is equal to 84.
Therefore, Statement-2 is true.
Explanation:
Statement-2 is a correct explanation for Statement-1 because the number of ways to distribute 10 identical balls in 4 distinct boxes such that no box is empty (286) is equal to the number of ways to choose any 3 places from 9 different places (84).
Hence, the correct answer is option 'D'.
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Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3 .Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3 . [2011]a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'D'. Can you explain this answer?
Question Description
Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3 .Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3 . [2011]a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3 .Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3 . [2011]a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3 .Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3 . [2011]a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'D'. Can you explain this answer?.
Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3 .Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3 . [2011]a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3 .Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3 . [2011]a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3 .Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3 . [2011]a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Statement-1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3 .Statement-2: The number of ways of choosing any 3 places from 9 different places is 9C3 . [2011]a)Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.b)Statement-1 is true, Statement-2 is false.c)Statement-1 is false, Statement-2 is true.d)Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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