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A box contains 6 distinct dolls. From this box, 3 dolls are randomly selected one by one with replacement. What is the probability of selecting 3 distinct dolls?
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Verified Answer
The correct answer is:
$5 / 9$
Required probability $=\frac{{ }^{6} \mathrm{C}_{1} \times{ }^{5} \mathrm{C}_{1} \times{ }^{4} \mathrm{C}_{1}}{{ }^{6} \mathrm{C}_{1} \times{ }^{6} \mathrm{C}_{1} \times{ }^{6} \mathrm{C}_{1}}$
$=\frac{6 \times 5 \times 4}{6 \times 6 \times 6}=\frac{5}{9}$
$=\frac{6 \times 5 \times 4}{6 \times 6 \times 6}=\frac{5}{9}$
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