Question

A man moves one unit distance for each step he takes. He always moves forward, backward, up or down their 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

• A. $280$
• B. $300$
• C. $360$
• D. $420$

Answer 1

Answer: (D)

$420$

There are only three possible ways to reach $(0,0)to(1,1)$

$\to$3 up 3 down and 1 forward =$\frac{6!}{3!2!}$

$\to$1 up and 3 forward 2 backward =$\frac{6!}{3!2!}$

$\to$2 up 1 down and 2 forward 1 backward =$\frac{6!}{3!3!}$

Adding the 3

we get

$\frac{6!}{3!2!}+$$\frac{6!}{3!2!}+$$\frac{6!}{3!3!}=140$

this the no. of ways is $\to 140\times 3=420$