A man moves one unit distance for each step he takes. He always moves forward, backward, up or down either parallel to the x-axis or y-axis.. He starts at the point ( 0 , 0 ) and reaches the point ( 1

Question

A man moves one unit distance for each step he takes. He always moves forward, backward, up or down either parallel to the x-axis or y-axis.. He starts at the point ( 0 , 0 ) and reaches the point ( 1 , 1 ) at the end of six steps. The number of ways he can do it is

TestHub · Accepted Answer

Let E, W, N, S stand for one unit movement along +ve, -ve, x-direction, +ve, -ve, y-direction respectively. The sequence of 6 steps are.

ENNNSS with $\frac{6 !}{3 ! 2 !} = 60$ ways

EEWNNS with $\frac{6 !}{2 ! 2 !} = 180$ ways

EEEWWN with $\frac{6 !}{3 ! 2 !} = 60$ ways

The desired number $= 60 + 180 + 60 = 300$

Mathematics - Permutation & Combination Question with Solution | TestHub

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