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With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4, 6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), is
Correct answer is '3920'. Can you explain this answer?
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With rectangular axes of coordinates, the number of paths from (1,1) ...
The number of paths from (1,1) to (8,10) via (4,6) = The number of paths from (1,1) to (4,6) * The number of paths from (4,6) to (8,10)
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To calculate the number of paths from (1,1) to (4,6), 4-1 =3 steps in x-directions and 6-1 =5 steps in y direction
Hence the number of paths from (1,1) to (4,6) = (3+5)C3 – 56
To calculate the number of paths from (4,6) to (8,10), 8-4 =4 steps in x-directions and 10-6=4 steps in y direction
Hence the number of paths from (4,6) to (8,10) = (4+4)C4 = 70
The number of paths from (1,1) to (8,10) via (4,6) = 56*70=3920
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With rectangular axes of coordinates, the number of paths from (1,1) ...
Number of Paths from (1,1) to (8,10) via (4,6)
Introduction:
In this problem, we are given a rectangular coordinate system and we need to find the number of paths from point (1,1) to point (8,10) while passing through point (4,6). We can only move in two directions - either right (x+1) or up (y+1).
Approach:
To solve this problem, we can break it down into smaller sub-problems. We can consider the number of paths from (1,1) to (8,10) as the sum of the number of paths from (1,1) to (4,6) and the number of paths from (4,6) to (8,10).
Step 1: Finding the number of paths from (1,1) to (4,6)
We can calculate this using the binomial coefficient formula. Since we need to move right 3 units (4-1) and up 5 units (6-1), the number of paths can be calculated as:
C(3+5, 5) = C(8, 5) = 8! / (5! * (8-5)!) = 56
Step 2: Finding the number of paths from (4,6) to (8,10)
Similarly, we need to move right 4 units (8-4) and up 4 units (10-6). Hence, the number of paths can be calculated as:
C(4+4, 4) = C(8, 4) = 8! / (4! * (8-4)!) = 70
Step 3: Finding the total number of paths
Now, we can find the total number of paths by multiplying the number of paths from (1,1) to (4,6) and the number of paths from (4,6) to (8,10):
56 * 70 = 3920
Conclusion:
Therefore, the correct answer is 3920, which represents the total number of paths from point (1,1) to point (8,10) while passing through point (4,6).
Introduction:
In this problem, we are given a rectangular coordinate system and we need to find the number of paths from point (1,1) to point (8,10) while passing through point (4,6). We can only move in two directions - either right (x+1) or up (y+1).
Approach:
To solve this problem, we can break it down into smaller sub-problems. We can consider the number of paths from (1,1) to (8,10) as the sum of the number of paths from (1,1) to (4,6) and the number of paths from (4,6) to (8,10).
Step 1: Finding the number of paths from (1,1) to (4,6)
We can calculate this using the binomial coefficient formula. Since we need to move right 3 units (4-1) and up 5 units (6-1), the number of paths can be calculated as:
C(3+5, 5) = C(8, 5) = 8! / (5! * (8-5)!) = 56
Step 2: Finding the number of paths from (4,6) to (8,10)
Similarly, we need to move right 4 units (8-4) and up 4 units (10-6). Hence, the number of paths can be calculated as:
C(4+4, 4) = C(8, 4) = 8! / (4! * (8-4)!) = 70
Step 3: Finding the total number of paths
Now, we can find the total number of paths by multiplying the number of paths from (1,1) to (4,6) and the number of paths from (4,6) to (8,10):
56 * 70 = 3920
Conclusion:
Therefore, the correct answer is 3920, which represents the total number of paths from point (1,1) to point (8,10) while passing through point (4,6).
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With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4, 6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), isCorrect answer is '3920'. Can you explain this answer?
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With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4, 6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), isCorrect answer is '3920'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4, 6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), isCorrect answer is '3920'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4, 6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), isCorrect answer is '3920'. Can you explain this answer?.
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