Assuming, in the absence of other information, that the probability that a claim is valid is 0.5, that is, there is an equal chance that it's valid or invalid, we let p=0.5 and q=1-p=0.5, then use the binomial expansion where n=15. Next we work out how many combinations there are of selecting exactly 10 claims out of 15: 3003 (this is 15×14×13×...×6/(10×9×8×...×1)=3003). 3003p10q5=3003/215=0.0916 approx, or 9.16%. This is the same as tossing a coin 15 times and getting 10 heads.
If p is different from 0.5 (empirical evidence: from past experience of what proportion of claims turn out to be valid), then the result will differ, that is, 3003p10q5 will have a different value.