A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, the probability of exactly 6 successes, is :

$35\left(\frac{1}{6}\right)^7$

The correct answer is Option (3) → $35\left(\frac{1}{6}\right)^7$

7 cases be obtained in following values → $(1, 6),(2,5),(3,4),(4,3),(5,2),(6,1)$

$P=\frac{6}{36}=\frac{1}{6}$

so P(6 successes) = ${^7C}_6(\frac{1}{6})^6(\frac{5}{6})$

$=7×5×(\frac{1}{6})^7=35×(\frac{1}{6})^7$