A fair die is thrown 20 times. The probability that on the 10th throw, the fourth six appears is `^20 C_(10)xx5^6//6^(20)` b. `120xx5^7//6^(10)` c. `84xx5^6//6^(10)` d. none of these

Options

A. `(""^(20)C_(10)xx5^(6))/(6^(20))`
B. `(120xx5^(7))/(6^(10))`
C. `(84xx5^(6))/(6^(10))`
D. None of these

Answer

C

Explanation

(c ) In the first nine throws, we should have three sixes and six non-sixes and a six in the tenth throw and thereafter, whatever face appear no matter.
`:.` Required probability
`=""^(9)C_(3)((1)/(6))^(3)xx((5)/(66))^(6)xx(1)/(6)xxunderset(10" times")underbrace(1xx1xx1xx…xx1)`
`=(84xx5^(6))/(6^(10))`