I'm generally good with math, but probability calculation just seems to fight me.

I'm trying to develop a formula to determine the odds of hitting at least 2 spades, given that the player is dealt their first 3 cards. 

The probability is about **15.05%**. I have confirmed this by running 5 million simulated 3 card hands and comparing how many times 2 or 3 spades hit. This is agrees with the online calculator here: <https://www.ohrt.com/odds/index.php?t[]=52&d[]=3&o[]=13&c[]=2&&s=any&p=9>

By my reasoning, the formula to arrive at the probability should be:

`combin(13,2)*combin(50,1)/combin(52,3)`

or "from 13 spades, take 2, from the remaining cards, take 1, and divide by the total number of 3 card combinations in a 52 card deck". 

But that gives me a result of 17.65%. 

I'm trying to develop a general formula for any number of outs or cards dealt(similar to the online calculator), but this was the test case I've been stuck on for a while.