# A bag contains 20 coins. If the probability that the bag contains exactly 4 biased coin is 1/3 and that of exactly 5 biased coin is 2/3, then the probability that all the biased coin are sorted out from the bag in exactly 10 draws is

Question : A bag contains 20 coins. If the probability that the bag contains exactly 4 biased coin is 1/3 and that of exactly 5 biased coin is 2/3, then the probability that all the biased coin are sorted out from the bag in exactly 10 draws is

(A) $\dfrac{5}{10}\cdot \dfrac{16C_{6}}{20C_{9}}+\dfrac{1}{10}\cdot \dfrac{15C_{5}}{20C_{9}}$

(B) $\dfrac{2}{33}\left[ \dfrac{16C_{6}+\left( 5\right) ^{15}C_{5}}{20C_{9}}\right]$

(C) $\dfrac{5}{33}\cdot \dfrac{16C_{6}}{20C_{9}}+\dfrac{1}{11}\cdot \dfrac{15C_{5}}{20C_{9}}$

(D) none of these

=\begin{aligned}\cdot \ \dfrac{1}{3}\cdot \dfrac{4C_{3}\cdot 16C_{6}}{20C_{9}}+\dfrac{2}{3}\cdot \dfrac{5C_{4}.15C_{5}}{20C_{9}}\cdot \dfrac{1}{11C_{1}}\end{aligned}
=$\dfrac{2}{33}\left[ \dfrac{16C_{6}+\left( 5\right) ^{15}C_{5}}{20C_{9}}\right]$