How many paths are there from point (0,0) to point (50,50) on the two-dimensional plane if each step along a path increments one coordinate and leaves the others unchanged and there is an impassable obstacle at the points (10, 11) and (20, 19)? Provide a formula representation of your result that includes binomial coefficients, and navigate the reader through the development of your formula.

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.