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When 8 dice (six-sided) are rolled, calculate the number of outcomes in which at least one die shows 5. 

Option: 1

1188901
 


Option: 2

1088891


Option: 3

1288991

 


Option: 4

1388910


Answers (1)

best_answer

Given that,

The dice are rolled 8 times.

The permutation with repetition is given by \mathrm{n^{r}}.

The total number of possible outcomes is \mathrm{6^{8}}.

Thus,

\begin{aligned} & 6^8=6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 \times 6 \\ & 6^8=1679616 \end{aligned}

The total number of outcomes, when no 5 appears, is 5^8.
\begin{aligned} & 5^8=5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \\ & 5^8=390625 \end{aligned}
So, the total number of possible outcomes is given by,
\begin{aligned} & 6^8-5^8=1679616-390625 \\ & 6^8-5^8=1288991 \end{aligned}
Therefore, the number of possible outcomes is 1288991 .

Posted by

himanshu.meshram

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