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# A fair die is tossed eight times. The probability that a third six is observed on the eight throw is

$\begin {array} {1 1} (A)\;\large\frac{7C_2 \times 5^5}{6^7} & \quad (B)\;\large\frac{7C_2 \times 5^5}{6^8} \\ (C)\;\large\frac{7C_2 \times 5^5}{6^6} & \quad (D)\;None\: of \: these \end {array}$

Required probability = $7C_2 \bigg(\large\frac{1}{6} \bigg)^2 \bigg(\large\frac{5}{6} \bigg)^5 \times \large\frac{1}{6}$
$= \large\frac{7C_2 \times 5^5}{6^8}$