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Given a Pokémon deck containing Salty, Sweet, Sour, Bitter, and Umami elemental cards, how many cards...

Given a Pokémon deck containing Salty, Sweet, Sour, Bitter, and Umami elemental cards, how many cards must you draw, face down, to be assured of drawing 5 of some elemental flavor?

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Answer #1

As we are drawing randomly here, to guarantee here of having 5 cards of the same elemental flavor is computed here as:

We take the worst possible case here, where for each of the five flavors we get 4 cards each that is we get a total of 20 cards here. Now the 21st card has to be one of the 5 flavor cards at which instant we will have 5 cards of the same flavor.

Therefore we need to pick up 21 cards to have a guarantee of getting 5 cards of the same flavor.

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