A bag contains 10 balls out of which k are red and ( 10-k ) are black, where 0 ≤ k ≤ 10. If three balls are drawn at random without replacement and…

A bag contains $\displaystyle 10$ balls out of which $\displaystyle k$ are red and ( $\displaystyle 10-k$ ) are black, where $\displaystyle 0 \leq k \leq 10$. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains $\displaystyle 1$ red and $\displaystyle 9$ black balls is: