Question

Four die are rolled. The number of ways in which at least one die shows $2$ is

• A. $546$
• B. $671$
• C. $625$
• D. $1256$

Answer 1

The correct option is B $671$

Number of dice rolled $=4$

Each dice has outcome $=6$

Total number of outcome of $4$ dice

$\Rightarrow {\left(6\right)}^4\Rightarrow 6\times 6\times 6\times 6\Rightarrow 1296$

Atleast one two so

Total outcome - number of two as a outcome

Number of outcome possible if two doesnt occur$=5$

on and dice

$\Rightarrow {\left(5\right)}^4\Rightarrow 5\times 5\times 5\times 5\Rightarrow 625$

Outcome possible when atleast one $2$ is possible

$\Rightarrow {\left(6\right)}^4-{\left(5\right)}^4\Rightarrow 1296-625\Rightarrow 671$