An urn has ten black ball numbered from 1 to 10 and ten white ball numbered from 1 to 10. > An urn has ten black ball numbered from 1 to 10 and ten white ball numbered from 1 to 10. > > how many ways can we choose five balls from the urn so that the numbers on the chosen balls are distinct Ans= $\binom{10}{5} * {2^5}$ why is $2^5$?

The $2^5$ comes from choosing the colors of the balls. The factor ${10 \choose 5}$ is the number of ways to choose which numbers will be represented, but you still haven't specified which ball of each number.