In a box there are 10 white ball and 10 black balls.Two balls are successively drawn.What is the probability to get two balls of different colors?
My interpretation is that the order doesn't matter, because the important is that the balls have different colors.So to find the possible cases I computed a combination, $^{20}C_{2}$. To find the favorable cases I multiplied $10$ white balls by $10$ black balls.
The final mathematical expression stays: $\frac{10^2 \cdot 2}{20 \cdot 19}$
The book's interpretation is the following:
For the possible cases, there are $20$ for the first ball and $19$ for the second.So there are $20 \cdot 19$ possible cases.Regarding the favorable cases the book says that there are $10 \cdot 10 \cdot 2$.
It's clear that by the book's interpretation the order matters.The two final mathematical expressions are the same.How can this happen if the interpretations were different?