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A restaurant is giving away three different toys with each child's meal. What is the probability of getting all the toys in purchasing five meals?

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    $\begingroup$ give your own initial thought please $\endgroup$
    – J Tg
    Sep 6, 2017 at 16:22

2 Answers 2

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Hint: Sufficient Condition for getting all 3 kinds of toys in 5 meals is that no single kind of toy appears 3 times or more.

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Choose any three space for $ toy_1 , toy_2 $ and $ toy_3 $ in $ \binom{5}{3} $ ways. And fill the 2 blank space with any possibility with $ 3^2 $ ways.

Total number of ways are: $ 3^5 $

Hence, required probability will be $ \frac{10}{27} $.

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