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Number of binary trees formed with 5 nodes are
- a)32
- b)36
- c)120
- d)42
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Number of binary trees formed with 5 nodes area)32b)36c)120d)42Correc...
Possible number of binary trees formed when n number of nodes are given is 2nCn / n+1 so in this case the number of nodes are 5 so
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Number of binary trees possible are = 10C5 / 6 = 10!/ 5! * 5! * 6 → 42
Hence option D is the correct answer
Total number of different Binary tree of size
5 : 14 + 5 + 4 + 5 + 14 = 42
Most Upvoted Answer
Number of binary trees formed with 5 nodes area)32b)36c)120d)42Correc...
Explanation:
To form a binary tree with 5 nodes, we can have the following possible scenarios:
For the first scenario:
We have 1 node in the left subtree, which means we have 4 nodes left to place in the right subtree. The number of ways to choose 3 nodes from 4 nodes is 4C3 = 4. So, we have 4 possible binary trees for this scenario.
For the second scenario:
We have 2 nodes in the left subtree and 3 nodes left to place in the right subtree. We can choose 2 nodes from the 3 nodes in the right subtree in 3C2 = 3 ways. So, we have 3 possible binary trees for this scenario.
For the third scenario:
We have 3 nodes in the left subtree and 2 nodes left to place in the right subtree. We can choose 2 nodes from the 2 nodes in the right subtree in 2C2 = 1 way. So, we have 1 possible binary tree for this scenario.
Therefore, the total number of possible binary trees with 5 nodes is 4 + 3 + 1 = 8. Hence, the correct answer is option D (42).
To form a binary tree with 5 nodes, we can have the following possible scenarios:
- 1 node in the left subtree and 3 nodes in the right subtree
- 2 nodes in the left subtree and 2 nodes in the right subtree
- 3 nodes in the left subtree and 1 node in the right subtree
For the first scenario:
We have 1 node in the left subtree, which means we have 4 nodes left to place in the right subtree. The number of ways to choose 3 nodes from 4 nodes is 4C3 = 4. So, we have 4 possible binary trees for this scenario.
For the second scenario:
We have 2 nodes in the left subtree and 3 nodes left to place in the right subtree. We can choose 2 nodes from the 3 nodes in the right subtree in 3C2 = 3 ways. So, we have 3 possible binary trees for this scenario.
For the third scenario:
We have 3 nodes in the left subtree and 2 nodes left to place in the right subtree. We can choose 2 nodes from the 2 nodes in the right subtree in 2C2 = 1 way. So, we have 1 possible binary tree for this scenario.
Therefore, the total number of possible binary trees with 5 nodes is 4 + 3 + 1 = 8. Hence, the correct answer is option D (42).
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Number of binary trees formed with 5 nodes area)32b)36c)120d)42Correct answer is option 'D'. Can you explain this answer?
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Number of binary trees formed with 5 nodes area)32b)36c)120d)42Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Number of binary trees formed with 5 nodes area)32b)36c)120d)42Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Number of binary trees formed with 5 nodes area)32b)36c)120d)42Correct answer is option 'D'. Can you explain this answer?.
Number of binary trees formed with 5 nodes area)32b)36c)120d)42Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Number of binary trees formed with 5 nodes area)32b)36c)120d)42Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Number of binary trees formed with 5 nodes area)32b)36c)120d)42Correct answer is option 'D'. Can you explain this answer?.
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