A ordinary cube has four plane faces, one face marked 2 and anoth… - Vidyadip

Question

A ordinary cube has four plane faces, one face marked 2 and another face marked 3, find the probability of getting a total of 7 in 5 throws.

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Answer

A cube has total 6 faces.
Total possible outcomes in 5 throws $= 6 \times 6\times 6 \times 6 \times 6 = (6)^5$
The only way of getting 7 is by getting two 2s and one 3.
Total possible ways $=\frac{\text{P}^5_3}{2!}$
$=\frac{5\times4\times3\times2\times1}{2\times1\times2\times1}$
$=30$
Now,
$P($getting $7$ in $5$ throws$)=\frac{30}{6^5}=\frac{5}{6^4}$

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