A path of length $n$ is a sequence of points $\left(x_1,y_1\right)$, $\left(x_2,y_2\right)$,….,$\left(x_n,y_n\right)$ with integer coordinates such that for all $i$ between $1$ and $n-1$ both inclusive,
either $x_{i+1}=x_i+1$ and $y_{i+1}=y_i$ (in which case we say the $i^{th}$ step is rightward)
or $x_{i+1}=x_i$ and $y_{i+1}=y_i+1$ ( in which case we say that the $i^{th}$ step is upward ).
This path is said to start at $\left(x_1,y_1\right)$ and end at $\left(x_n,y_n\right)$. Let $P\left(a,b\right)$, for $a$ and $b$ non-negative integers, denotes the number of paths that start at $\left(0,0\right)$ and end at $\left(a,b\right)$.
The sum $P\left(43,4\right)+\sum _{j=1}^{5}P\left(49-j,3\right)$ is equal to

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