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  • Calculate the number of possible outcomes where at least one die displays 6 when 4 dice (six-sided) are rolled.   Option: 1 561</

Calculate the number of possible outcomes where at least one die displays 6 when 4 dice (six-sided) are rolled. 

 

Option: 1

561


Option: 2

491


Option: 3

671


Option: 4

891


Answers (1)

best_answer

Given that,

The dice are rolled 4 times.

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

The total number of possible outcomes is 6^{4} .

Thus,

\begin{aligned} & 6^4=6 \times 6 \times 6 \times 6 \\ & 6^4=1296 \end{aligned}

The total number of outcomes when no 6 appears is 5^{8}.

\begin{aligned} & 5^4=5 \times 5 \times 5 \times 5 \\ & 5^4=625 \end{aligned}

So, the total number of possible outcomes is given by,

\begin{aligned} & 6^4-5^4=1296-625 \\ & 6^4-5^4=671 \end{aligned}

Therefore, the number of possible outcomes is 671.

 

Posted by

Pankaj

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