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If the number of ways in which four distinct balls can be put into two identical boxes such that no box remains empty is equal to k, then k is
Correct answer is '7'. Can you explain this answer?
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Most Upvoted Answer
If the number of ways in which four distinct balls can be put into tw...
Explanation:
Understanding the Problem:
When putting four distinct balls into two identical boxes, we need to ensure that no box remains empty. This means each box must have at least one ball.
Approach:
To solve this problem, we can use the concept of stars and bars. We have 4 distinct balls, and we need to distribute them into 2 identical boxes, ensuring each box has at least one ball. This can be represented as placing 2 dividers among the 4 balls.
Calculation:
The number of ways to distribute the balls can be calculated using the formula (n + r - 1)C(r), where n is the number of objects to distribute (4 balls), r is the number of containers (2 boxes), and C represents combinations.
Plugging in the values, we get:
(4 + 2 - 1)C(2) = 5C2 = 10
However, since the boxes are identical, we need to divide by 2 to avoid counting the same distribution twice. So, the final number of ways is:
10 / 2 = 5
Final Answer:
Therefore, the number of ways in which four distinct balls can be put into two identical boxes such that no box remains empty is 5.
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Community Answer
If the number of ways in which four distinct balls can be put into tw...
Every ball has two options
⇒ 4 balls can be put in 24 ways.
Arrangement among themselves is 2!
But, above count also includes the one case in which all the balls are put in one box,
⇒ required number of ways k = 23 −1 = 7
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If the number of ways in which four distinct balls can be put into two identical boxes such that no box remains empty is equal to k, then k isCorrect answer is '7'. Can you explain this answer?
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If the number of ways in which four distinct balls can be put into two identical boxes such that no box remains empty is equal to k, then k isCorrect answer is '7'. 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 If the number of ways in which four distinct balls can be put into two identical boxes such that no box remains empty is equal to k, then k isCorrect answer is '7'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the number of ways in which four distinct balls can be put into two identical boxes such that no box remains empty is equal to k, then k isCorrect answer is '7'. Can you explain this answer?.
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