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There are 12 different marbles to be divided between 2 different childrenin the ratio 1: 2. The number of ways this can be done is?
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There are 12 different marbles to be divided between 2 different child...
Understanding the Problem
When dividing 12 different marbles between 2 children in a ratio of 1:2, we need to assign the marbles such that one child receives one part and the other receives two parts of the total.
Calculating the Distribution
- Total parts = 1 + 2 = 3 parts.
- Each part consists of \( \frac{12}{3} = 4 \) marbles.
- Thus, Child A will receive 4 marbles (1 part), and Child B will receive 8 marbles (2 parts).
Choosing Marbles for Each Child
- Choosing for Child A: We need to select 4 marbles from the 12 available.
The number of ways to choose 4 marbles from 12 is calculated using the combination formula:
\[
\text{Number of ways} = \binom{12}{4} = \frac{12!}{4!(12-4)!}
\]
Calculating the Combination
- Using the combination formula:
\[
\binom{12}{4} = \frac{12 \times 11 \times 10 \times 9}{4 \times 3 \times 2 \times 1} = 495
\]
- Assigning Marbles to Child B: Once 4 marbles are chosen for Child A, the remaining 8 marbles automatically go to Child B.
Final Calculation
The total number of ways to distribute the marbles is simply the number of ways to choose marbles for Child A, which is 495.
Conclusion
Thus, the total number of ways to divide 12 different marbles between 2 different children in the ratio of 1:2 is 495.
When dividing 12 different marbles between 2 children in a ratio of 1:2, we need to assign the marbles such that one child receives one part and the other receives two parts of the total.
Calculating the Distribution
- Total parts = 1 + 2 = 3 parts.
- Each part consists of \( \frac{12}{3} = 4 \) marbles.
- Thus, Child A will receive 4 marbles (1 part), and Child B will receive 8 marbles (2 parts).
Choosing Marbles for Each Child
- Choosing for Child A: We need to select 4 marbles from the 12 available.
The number of ways to choose 4 marbles from 12 is calculated using the combination formula:
\[
\text{Number of ways} = \binom{12}{4} = \frac{12!}{4!(12-4)!}
\]
Calculating the Combination
- Using the combination formula:
\[
\binom{12}{4} = \frac{12 \times 11 \times 10 \times 9}{4 \times 3 \times 2 \times 1} = 495
\]
- Assigning Marbles to Child B: Once 4 marbles are chosen for Child A, the remaining 8 marbles automatically go to Child B.
Final Calculation
The total number of ways to distribute the marbles is simply the number of ways to choose marbles for Child A, which is 495.
Conclusion
Thus, the total number of ways to divide 12 different marbles between 2 different children in the ratio of 1:2 is 495.
Community Answer
There are 12 different marbles to be divided between 2 different child...
12P4*8P8
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There are 12 different marbles to be divided between 2 different childrenin the ratio 1: 2. The number of ways this can be done is?
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There are 12 different marbles to be divided between 2 different childrenin the ratio 1: 2. The number of ways this can be done is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about There are 12 different marbles to be divided between 2 different childrenin the ratio 1: 2. The number of ways this can be done is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 12 different marbles to be divided between 2 different childrenin the ratio 1: 2. The number of ways this can be done is?.
There are 12 different marbles to be divided between 2 different childrenin the ratio 1: 2. The number of ways this can be done is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about There are 12 different marbles to be divided between 2 different childrenin the ratio 1: 2. The number of ways this can be done is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are 12 different marbles to be divided between 2 different childrenin the ratio 1: 2. The number of ways this can be done is?.
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