Question

A man standing at a point P on a flat plane starts walking. At each step, he walks exactly 1 foot in one of the directions N,S,E or W. Suppose that after 6 steps he comes back to P, then no. of distinct paths he can take is ?

a) 196
b)256
c)344
d)400

Answer 1

I have attempted this and am getting 384 as the answer.
But 384 is not even in the options -_-

I'll post my attempt below

Answer 2

lets divide 6 steps into 2 cases
first 3 and last 3
for him to be back at original pos
there should be 3 counter steps

E and W are counter
N and S are counter

for 1st 3 steps
he has 4 options of each step
so 4*4*4
=64
now for last 3 steps, we need 3 counter steps ..
the 3 counter steps can be at any position..
so 3! i.e. 6
final ans acc to me should have been 64*6 = 384

but thats wrong
where am I going wrong ?

Answer 3

u have 288 in options ?

Answer 4

I have posted the options
no, 288 is not there @ganeshie8

Answer 5

seems like I am getting 404
http://www.wolframalpha.com/input/?i=Sum%5BBinomial%5B3%2Ck%5D%5E2%2C%7Bk%2C+0%2C+3%7D%5D*4+%2B4*9%5E2

Answer 6

woops!! i counted double ... 400

Answer 7

please explain your logic sir :O
yes 400 is the right ans

Answer 8

just consider the position of third step.

Answer 9

x is where your possible third step is