There are 10 different billiard balls are there, how many ways of choosing them by 2 are there so that when you take it you don't put it back?
o you mean:
There are 10 billiard balls
One is taken and not returned.
Then a second one is taken.
How many ways can the two be taken?
there are 10 ways that the first one can be taken and then 9 ways the second one can be taken so that is
10*9 = 90 ways
Note: If order does not matter then you will have to divide this by 2 and get 45 ways.