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# 10 6-sided dice are rolled

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Ten 6-sided dice are rolled. What is the probability that exactly three of the dice show a 1? Express your answer as a decimal rounded to the nearest thousandth.

thanks!

Sep 6, 2017

#1
+22188
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Ten 6-sided dice are rolled. What is the probability that exactly three of the dice show a 1?

thanks!

$$\begin{array}{|rcll|} \hline && \binom{10}{3} \times \left(\frac16 \right)^3 \times \left(\frac56 \right)^7 \\\\ &=& \frac{120 \times 5^7 }{6^{10}} \\ \\ &=& \frac{9375000}{60466176} \\ \\ &=& 0.15504535957 \ (15.5 \% ) \\ \hline \end{array}$$

$$\begin{array}{lcll} \text{possibilities: 10 dices, three "1" } &=& \binom{10}{3} \\ \text{probability: 3dices, three "1" } &=& \left(\frac16 \right)^3 \\ \text{probability: 7dices, no "1" } &=& \left(\frac56 \right)^7 \\ \end{array}$$

Sep 7, 2017