Question

Four dice are rolled. The number of possible out comes in which atleast one die shows $2$ is

• A. $1296$
• B. $625$
• C. $615$
• D. $671$

Answer 1

Answer: (D)

$671$

The dice has $6$ faces using the numbers $1,2,...,6$

i.e., it has $6$ possible out comes when four dices as rolled, thenumber of possible out comes $=6\times 6\times 6\times 6$ [product rule]

The number of possible out comes in which $2$ does not appear on any dice $=5^4$ ($2$ is absent)

Hence, using the relation, atleast one $=$ general $-$ none

The number of possible out comes in which at least one dice shows ${}^{\prime }{2}^{\prime }$

$=6^4-5^4=1296-625=671$