Mr. A lives at origin on the Cartesian plane and has his office at (4, 5). His friend lives at (2, 3) on the same plane. Mr. A can go to his office traveling one block at a time either in the +y or +x direction. If all possible paths are equally likely then the probability that Mr. A passed his friends house is (shortest path for any event must be considered)

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1/2

10/21

1/4

11/21

answer is B.

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Detailed Solution

n(S)=9!4!.5!=126n(A)=O to F and F to P=5!2!×3!×4!2!×2!=60⇒ P(A)=60126=1021

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