How many ways are there to move from the origin to $(a,b)$ where $a$ and $b$ are positive integers and you can only move up or right one unit at a time???????
The number of ways is \(\dfrac{(a + b)!}{a!}\)
Actually, it's $\displaystyle {{a+b}\choose{a}} = \frac{(a+b)!}{a!b!}$. Get it right.
