Question

A person is to walk from $A$ to $B$. However, he is restricted to walk only to the right of $A$ or upwards of $A$, but not necessarily in the order shown in the figure. Then find the number of paths from $A$ to $B$.

Answer 1

In givem figure

Total number of squares in right of A and upwards A $=5+4=9$

Number of ways possible from A to B by edges upwards of A$={}^9{C}_5=\frac{9!}{5!4!}=\frac{9\times 8\times 7\times 6}{4\times 3\times 2\times 1}=126$