>>1556173the chance of 10 multiplied by the chance of 10 multiplied by the chance of not-10 gives you the chance of each individual arrangement of 2 successes and 1 failure, in this case, SSF
you then need to multiply this by the number of possible arrangements of 2 successes and 1 failure, which is three
SSF
SFS
FSS
thus 3 x 0.1 x 0.1 x 0.9 = 0.027
also, you're wrong about the chance of 1 ten. your formula gives 0.271, but the correct formula (same as above) gives 0.243. yours is the chance of AT LEAST ONE 10.
the full formula is here
https://en.wikipedia.org/wiki/Negative_binomial_distribution#Probability_mass_function