Useful resource to solve these problems: https://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/

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Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$.

How many distinct paths are there for the robot to reach the point $(10,10)$ starting from the initial position $(0,0)$?

- $^{20}\mathrm{C}_{10}$
- $2^{20}$
- $2^{10}$
- None of the above

Useful resource to solve these problems: https://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/

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To reach from $(0,0)$ to $(10,10)$ we have to take 20 steps.

Lets assume these 20 steps to be 20 places.

( _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ )

Out of these 20 places to have to choose 10 places for upper steps, the rest of the 10 places have to be for right steps.)

like one example is ( _ u u _ _ u _ _ u _ _uuu_ _u_u_ _ _ _ u), the $‘– ‘$ places should be for right steps.

so, Option $A$ $2nCn$ is the answer.

Lets assume these 20 steps to be 20 places.

( _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ )

Out of these 20 places to have to choose 10 places for upper steps, the rest of the 10 places have to be for right steps.)

like one example is ( _ u u _ _ u _ _ u _ _uuu_ _u_u_ _ _ _ u), the $‘– ‘$ places should be for right steps.

so, Option $A$ $2nCn$ is the answer.

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