I'm not understanding combinations and counting The question:
An urn has 10 black balls numbered from 1 to 10, and 10 white balls numbered from 1 to 10. In how many ways can we choose 5 balls from the urn?
(There are more questions, which is why there's balls that are different colors and numbered. This is just one of the)
I did answer ${20 \choose 5}$ which is the correct answer. But I don't know why, other than the word choose being in the question. 
Intuitively, I don't understand why $20 \times 19 \times 18 \times 16 \times 17$ isn't an answer for this question. I know it's incorrect and that they're very different answers, but I don't know why. My thinking is that the first ball you choose, you pick out of 20 possible choices, then there's 19, then 18, then 17 choices to pick from. 

You have to choose $5$ balls from $20$ balls; so the order of the balls does not matter. There are $20×19×18×17×16 $ number of ways contains only  $\frac{20×19×18×17×16 }{5!}$ different combinations of the balls. Although,if order of the drawn balls did matter,then yours would be the correct answer.
