Question

In a game, five die are rolled. The number of ways in which at least $2$ die shows $6$ is,

• A. $671$
• B. $4026$
• C. $1296$
• D. $3412$

Answer 1

Answer: (B)

$4026$

Number of dice rolled : $5$

Atleast $2$ dices show $6$

Total out come - no $6$ - only $6$

Total outcome on 1 dice $=6$

on $5$ dice $=6\times 6\times 6\times 6\times 6\times 6$

one six

one dice has only one outcome thatis $6$

Rest $4$ have $6$ outcome each

$\Rightarrow {\left(6\right)}^4$ Outcome

Outcome with atlest $6$ Outcomes

$\Rightarrow {\left(6\right)}^5-{\left(5\right)}^5-{\left(6\right)}^4\Rightarrow {\left(6\right)}^4(6-1)-{\left(5\right)}^5=({\left(5\right)}^5-{\left(5\right)}^5)6=4026$

Hence the correct answer is $4026$