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In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?
Correct answer is '6'. Can you explain this answer?
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In how many ways can 8 identical pens be distributed among Amal, Bimal...
Number of pens that Amal gets = a+1
Number of pens that Bimal gets = b+2
Number of pens that Kamal gets = k+3
So, (a+1) + (b+2) + (k+3) = 8
a + b + k = 2
So, we get (2+3-1)C(3-1) = 6 [Based on the formula, (n+r-1)C(r-1)]
Answer: 6
Number of pens that Bimal gets = b+2
Number of pens that Kamal gets = k+3
So, (a+1) + (b+2) + (k+3) = 8
a + b + k = 2
So, we get (2+3-1)C(3-1) = 6 [Based on the formula, (n+r-1)C(r-1)]
Answer: 6
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In how many ways can 8 identical pens be distributed among Amal, Bimal...
Solution:
To solve this problem, we will use the concept of the stars and bars method.
In this method, we first distribute the minimum number of pens required for each person. Then we distribute the remaining pens among the three persons.
Step 1: Distribute minimum pens
- Amal gets at least 1 pen
- Bimal gets at least 2 pens
- Kamal gets at least 3 pens
Therefore, we have distributed 1+2+3=6 pens. We have 2 pens remaining to distribute among the three persons.
Step 2: Distribute remaining pens
We can distribute the remaining 2 pens in the following ways:
- Amal gets 1 pen, Bimal gets 1 pen, and Kamal gets 0 pens
- Amal gets 1 pen, Bimal gets 0 pens, and Kamal gets 1 pen
- Amal gets 0 pens, Bimal gets 1 pen, and Kamal gets 1 pen
- Amal gets 0 pens, Bimal gets 2 pens, and Kamal gets 0 pens
- Amal gets 2 pens, Bimal gets 0 pens, and Kamal gets 0 pens
- Amal gets 0 pens, Bimal gets 0 pens, and Kamal gets 2 pens
Therefore, there are 6 ways to distribute 8 identical pens among Amal, Bimal, and Kamal such that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens.
Final Answer: 6.
To solve this problem, we will use the concept of the stars and bars method.
In this method, we first distribute the minimum number of pens required for each person. Then we distribute the remaining pens among the three persons.
Step 1: Distribute minimum pens
- Amal gets at least 1 pen
- Bimal gets at least 2 pens
- Kamal gets at least 3 pens
Therefore, we have distributed 1+2+3=6 pens. We have 2 pens remaining to distribute among the three persons.
Step 2: Distribute remaining pens
We can distribute the remaining 2 pens in the following ways:
- Amal gets 1 pen, Bimal gets 1 pen, and Kamal gets 0 pens
- Amal gets 1 pen, Bimal gets 0 pens, and Kamal gets 1 pen
- Amal gets 0 pens, Bimal gets 1 pen, and Kamal gets 1 pen
- Amal gets 0 pens, Bimal gets 2 pens, and Kamal gets 0 pens
- Amal gets 2 pens, Bimal gets 0 pens, and Kamal gets 0 pens
- Amal gets 0 pens, Bimal gets 0 pens, and Kamal gets 2 pens
Therefore, there are 6 ways to distribute 8 identical pens among Amal, Bimal, and Kamal such that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens.
Final Answer: 6.
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In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?Correct answer is '6'. Can you explain this answer?
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In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?Correct answer is '6'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?Correct answer is '6'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?Correct answer is '6'. Can you explain this answer?.
In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?Correct answer is '6'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?Correct answer is '6'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?Correct answer is '6'. Can you explain this answer?.
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