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In a deck of 52 cards, each card is one of 4 different color

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In a deck of 52 cards, each card is one of 4 different color  [#permalink]

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New post 28 Aug 2009, 17:21
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In a deck of 52 cards, each card is one of 4 different colors and there are 13 cards of each color. If cards are to be selected at random from the deck, what is the least number of cards that must be selected to ensure that these are at least 3 cards of each color among selected?
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Re: Least # of cards  [#permalink]

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New post 28 Aug 2009, 20:38
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konayuki wrote:
42 is right... but I do not get it.

Help me with the logic!


The logic is the following.
The worst case scenario is that you draw the first 13 cards of the same colour, then another 13 of the same color then another 13 of the same color. After 39 cards, you draw all 3 colors. Then to ensure that you have at least 3 of each, you need to take another 3 cards of the 4th left colour. So in total after 42 card you can be sure you have at least 3 cards of each color (since we considered here the worst case scenario).

By the same logic, if you are asked how many cards you have to draw to ensure you have three of the same colour (not 3 of EACH), the answer is 9.
Here the worst case scenario is that you draw first 4 cards of different colour, then another 4 of different color. After 8 cards, you have two of each colour. So when you draw the 9th card, you are sure you have at least 3 cards of the same colour.
Hope this helps.
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Re: Least # of cards  [#permalink]

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New post 28 Aug 2009, 18:51
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nikhilpoddar wrote:
42

Thanks. I didn't notice they ask about three of EACH color. I thought they ask about first three of the same color...If three of each, it is 42.
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Re: Least # of cards  [#permalink]

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New post 28 Aug 2009, 20:00
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42 is right... but I do not get it.

Help me with the logic!
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In a deck of 52 cards, each card is one of 4 different color  [#permalink]

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New post 08 Aug 2015, 07:36
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konayuki wrote:
In a deck of 52 cards, each card is one of 4 different colors and there are 13 cards of each color. If cards are to be selected at random from the deck, what is the least number of cards that must be selected to ensure that there are at least 3 cards of each color among selected?


Total Cards to be picked (In Worst Case scenario) = 13(All card of First color)+13(All card of Second color)+13(all card of Third color)+2(Both card of Forth color)

i.e. Total cards Picked = 41 and still We don't have 3 cards of each colour

Butthe next card picked will be of forth color and then we will have atleast 3 cards of each colours

i.e. Minimum cards to be picked to ensure the desired scenario = 41+1 = 42 cards
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Re: In a deck of 52 cards, each card is one of 4 different color  [#permalink]

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New post 30 Aug 2018, 06:16
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