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Determine the number of outcomes in which at least one die shows 3 when 5 dice (six faced) are rolled.       

 

Option: 1

4561


Option: 2

3551


Option: 3

2651


Option: 4

4651


Answers (1)

best_answer

Given that,

The dice are rolled 5 times.

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

The total number of possible outcomes is 6^{5}.

Thus,

\begin{aligned} &6^5=6 \times 6 \times 6 \times 6 \times 6\\ &6^5=7776 \end{aligned}

The total number of outcomes, when no 3 appears, is 5^{5} .

\begin{aligned} & 5^5=5 \times 5 \times 5 \times 5 \times 5 \\ & 5^5=3125 \end{aligned}

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

\begin{aligned} &6^5-5^5=7776-3125\\ &6^5-5^5=4651 \end{aligned}

Therefore, the number of possible outcomes is 4651.

 

Posted by

Suraj Bhandari

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