Q85

MCQ2 marks, −0.5

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 $(i,j + 1)$ . Suppose that the robot is not allowed to traverse the line segment from $(4,4)$ to $(5,4)$ . With this constraint, how many distinct paths are there for the robot to reach $(10,10)$ starting from $(0,0)$ ?

(A)

$2^9$

(B)

$2^{19}$

(C)

$^{8}\mathrm{C}_{4} \times^{11}\mathrm{C}_{5}$

(D)

$^{20}\mathrm{C}_{10} - ^{8}\mathrm{C}_{4}\times ^{11}\mathrm{C}_{5}$

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