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Previous Year Question (PYQs)



How many different paths in the $xy$-plane are there from $(1,3)$ to $(5,6)$, if a path proceeds one step at a time either right (R) or upward (U)?





Solution

Right steps = $5-1 = 4$ 
Up steps = $6-3 = 3$ 
 Total steps = $7$ 
 Number of paths = $\binom{7}{3} = 35$


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