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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???????

 Dec 1, 2022
 #1
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The number of ways is \(\dfrac{(a + b)!}{a!}\)

 Dec 1, 2022
 #2
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Actually, it's $\displaystyle {{a+b}\choose{a}} = \frac{(a+b)!}{a!b!}$. Get it right.

Guest Dec 1, 2022

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