Question

Four dice are rolled. The number of ways in which atleast one die shows $3$, is

• A. $625$
• B. $671$
• C. $1296$
• D. $1256$

Answer 1

Answer: (B)

$671$

Number of ways in which any number appearing in one dice is $6$

Number of ways in which $3$ appear in one dice is $1$

Number of ways in which $3$ does not appear in one dice is $5$

There are $4$ dice.

Getting $3$ in atleast one dice $=$

Getting any number in all the $4$ dice - Not getting $3$ in any of the $4$ dice.

$=(6\times 6\times 6\times 6)-(5\times 5\times 5\times 5)$

$=1296-625$

$=671$