Question

In the figure given, a person can move either towards right or in upward direction only.

The number of different ways to reach the point $B$ from point $A$ is

Answer 1

At every position in the journey, person will have two possible paths i.e., either he can move rightword or upward.
Let horizontal movement be written as $H$ and vertical movement be written as $V$.


From above diagram, some of the possible paths are
HHHHVVVV and HV HV HV HV
Hence, every path is basically arrangement of $4$ H and $4$ V.
$\therefore$ Total number of ways to reach $B$ $=\frac{8!}{4!4!}$
$=\frac{8\times 7\times 6\times 5\times 4}{4\times 3\times 2\times 1\times 4}=70$