isi-entrance 2010 Q18

isi-entrance · India · solved Permutations & Arrangements Lattice Path / Grid Route Counting
A person $X$ standing at a point $P$ on a flat plane starts walking. At each step, he walks exactly 1 foot in one of the directions North, South, East or West. Suppose that after 6 steps $X$ comes to the original position $P$. Then the number of distinct paths that $X$ can take is
(a) 196
(b) 256
(c) 344
(d) 400
A person $X$ standing at a point $P$ on a flat plane starts walking. At each step, he walks exactly 1 foot in one of the directions North, South, East or West. Suppose that after 6 steps $X$ comes to the original position $P$. Then the number of distinct paths that $X$ can take is\\
(a) 196\\
(b) 256\\
(c) 344\\
(d) 400