A path of length n is a sequence of points (x_(1),y_(1)), (x_(2),y | Filo
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Class 12

Math

Algebra

Binomial Theorem

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A path of length is a sequence of points , ,…., with integer coordinates such that for all between and both inclusive,
either and (in which case we say the step is rightward)
or and ( in which case we say that the step is upward ).
This path is said to start at and end at . Let , for and non-negative integers, denotes the number of paths that start at and end at .
Number of ordered pairs where for which is

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