# A bag contains 20 coins. If the probability that 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 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) $\dfrac{5}{33}\dfrac{16C_{6}}{20C_{q}}+\dfrac{1}{11}\dfrac{15C_{5}}{20C_{9}}$

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

(C) $\dfrac{5}{33}\dfrac{16C_{7}}{20C_{9}}+\dfrac{1}{11}\dfrac{15_{C_{6}}}{20C_{9}}$

(D) none of these