Question 534794
The previous solution was almost correct with a little flaw in counting.

So you want the number of permutations of size 10 from 50, with replacement. 
This is just 50^10, or n^r.

Then you need to find the number of PERMUTATIONS without replacement, as this
will give you the numbers of ways you can rearrange 10 distinct object picked
from 50.
This is 50P10, nPr.

Then the probability of drawing 10 balls and not getting any matches is 
50P10/50^10

This is the complement of what you're actually looking for, so subtract this
value from 1
1 - 50P10/50^10

The numerical value is 0.61829331945.