Mr. A lives at origin on the Cartesian plane and has his office at `(4,5)dot` His friend lives at `(2,3)` on the same plane. Mrs. A can go to his office travelling one block at a time either in the `+yor+x` idrectin. 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 consider4ed) `1//2` b. `10//21` c. `1//4` d. `11//21`

Options

A. `1//2`
B. `10//21`
C. `1//4`
D. `11//21`

Answer

B

Explanation

`n(S) = (9!)/(4!.5!) =126`
n(A) = O to F and F to P
= `(5!)/(2! xx 3!) xx (4!)/(2! xx 2!) = 60`
`implies P(A) = (60)/(126) = (10)/(21)`