@RZ923 This is a great explanation.

Yes, it's sort of like this: "As the numbers towards the middle get bigger, then the ones even more toward the middle get even bigger..."

This uses the basic rule of Pascal's Triangle: To get any of the numbers in Pascal's Triangle, simply add the two numbers above it. So we get the following:

$$ \binom{1}{0} + \binom{1}{1} = \binom{2}{1} $$

$$ \binom{3}{1} + \binom{3}{2} = \binom{4}{2}$$

$$ \binom{5}{2} + \binom{5}{3} = \binom{6}{3} $$

$$ \text{ etc. } \ldots $$

That's a heuristic ("hand-wavy") kind of an argument which isn't very rigorous, but also shows why the numbers get bigger as you go towards the middle of Pascal's Triangle!