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Ten identical chocolates are to be distributed among five children - V, W, X, Y, and Z. What is the number of ways of distributing it so that only two children get exactly two chocolates each while the rest could get any number of chocolates?
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Ten identical chocolates are to be distributed among five children - V...
The problem:
We need to distribute ten identical chocolates among five children - V, W, X, Y, and Z. The distribution should be such that only two children get exactly two chocolates each, while the rest can get any number of chocolates.

Approach:
To solve this problem, we can break it down into different cases based on the number of chocolates received by the remaining three children - Y, Z, and W. Let's consider each case separately:

Case 1: Y, Z, and W receive 0 chocolates each.
In this case, V and X are the only two children who receive two chocolates each. The remaining six chocolates can be distributed in various ways among V, X, Y, Z, and W.

- The first chocolate can be given to any of the five children.
- The second chocolate can be given to any of the remaining four children.
- The third chocolate can be given to any of the remaining three children.
- The fourth chocolate can be given to any of the remaining two children.
- The fifth chocolate can be given to any of the remaining one child.
- The sixth chocolate will be automatically given to the last remaining child.

Therefore, the number of ways to distribute six chocolates among five children (assuming Y, Z, and W receive 0 chocolates each) is 5 * 4 * 3 * 2 * 1 = 120.

Case 2: Y receives 1 chocolate, while Z and W receive 0 chocolates each.
In this case, V and X receive two chocolates each. Y receives one chocolate, and Z and W receive 0 chocolates each. The remaining five chocolates can be distributed among V, X, Y, Z, and W.

- The first chocolate can be given to any of the five children.
- The second chocolate can be given to any of the remaining four children.
- The third chocolate can be given to any of the remaining three children.
- The fourth chocolate can be given to any of the remaining two children.
- The fifth chocolate will be automatically given to the last remaining child.

Therefore, the number of ways to distribute five chocolates among five children (assuming Y receives 1 chocolate, and Z and W receive 0 chocolates each) is 5 * 4 * 3 * 2 = 120.

Case 3: Y and Z receive 1 chocolate each, while W receives 0 chocolates.
In this case, V and X receive two chocolates each. Y and Z receive one chocolate each, and W receives 0 chocolates. The remaining four chocolates can be distributed among V, X, Y, Z, and W.

- The first chocolate can be given to any of the five children.
- The second chocolate can be given to any of the remaining four children.
- The third chocolate can be given to any of the remaining three children.
- The fourth chocolate will be automatically given to the last remaining child.

Therefore, the number of ways to distribute four chocolates among five children (assuming Y and Z receive 1 chocolate each, and W receives 0 chocolates) is 5 * 4 * 3 = 60.

Case 4: Y, Z, and W receive 1 chocolate each.
In this case, V and X receive two chocolates each. Y, Z, and W receive one chocolate each. The
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Ten identical chocolates are to be distributed among five children - V, W, X, Y, and Z. What is the number of ways of distributing it so that only two children get exactly two chocolates each while the rest could get any number of chocolates?
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Ten identical chocolates are to be distributed among five children - V, W, X, Y, and Z. What is the number of ways of distributing it so that only two children get exactly two chocolates each while the rest could get any number of chocolates? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Ten identical chocolates are to be distributed among five children - V, W, X, Y, and Z. What is the number of ways of distributing it so that only two children get exactly two chocolates each while the rest could get any number of chocolates? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ten identical chocolates are to be distributed among five children - V, W, X, Y, and Z. What is the number of ways of distributing it so that only two children get exactly two chocolates each while the rest could get any number of chocolates?.
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