A bag contains 20 coins. If the probability that the bag contains exactly 4 biased coin is 3/4 and that of exactly 5 biased coin is 2/3, then the probability that all the biased coin are sorted out from bag is exactly 10 draws is `5/(10)(^(16)C_6)/(^(20)C_9)+1/(11)(^(15)C_5)/(^(20)C_9)` b. `2/(33)[(^(16)C_6+5^(15)C_5)/(^(20)C_9)]` c. `5/(33)(^(16)C_7)/(^(20)C_9)+1/(11)(^(15)C_6)/(^(20)C_9)` d. none of these

Options

A. `(5)/(33) (.^(16)C_(8))/(.^(20)C_(9))+(1)/(11)(.^(15)C_(5))/(.^(20)C_(9))`
B. `(2)/(33)[(2^(16)C_(6)+5^(15)C_(5))/(.^(20)C_(9))]`
C. `(5)/(33)(.^(16)C_(7))/(.^(20)C_(9))+(1)/(11)(.^(15)C_(6))/(.^(20)C_(9))`
D. none of these

Answer

B