Not many AP's and honors.. still chance at Ivy League?

So my school is extremely small and doesn't offer many AP courses or all that many Honors classes either...

They offer:

AP's-

Biology

Calculus AB

Calculus BC

and they maaay start

Physics and Chemistry, but it's not 100 percent certain. (they're trying to offer it, but they're not sure if their budget will cover it)

I'm definitely taking AP Biology and AP Calculus AB, but not AP Calculus BC... If they end up offering AP Physics and Chem, then i'll definitely take those as well...

Even if they do offer those; it's still only 4 AP's, which is pretty horrible for an Ivy League if you ask me... Am I right?

As for honors-

Well we actually do have alot of honors, however there is NO option for science honors. There's no Biology Honors or Chem honors or Physics honors, which alot of people have the option of taking.

We have honors english for all 4 years; honors world history for 2, honors US History for 1; and Honors Government.

As for math classes, i think there's honors geometry and trig... Not sure about Algebra...

Out of either 8 or 9 honors classes, i'm taking/ I took 5.

4 AP's and 5 honors classes... Any chance at an Ivy League at all?

The ivy league I'm looking into the most is Columbia...

*One of the honors classes I only got an 83 average though, so that probably shouldn't even count...

Another thing... At one of the SUNY schools nearby, they have this program where high school students can take a college course during the summer... I'm probably taking at least 1 course; probably 2 or 3 though... Assuming I do well, could this also help my chance at admissions?

BE HONEST PLEASE!!!