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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 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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konayuki
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?

42.

worst case + 1

(13+13+13+2)+1
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This is a worst case scenario , so consider picking 13 cards from 3 color , even then we would not have selected 3 cards from all colours.

So, we have 13 from 3 colors, so 3*13 = 39
Plus 3 from 4th color , so in total we have 39+3 = 42

Ans: 42
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konayuki
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?

A. 40
B. 41
C. 42
D. 43
E. 44
­
To ensure that at least 3 cards of each color are selected, we could select 13 of one color, then 13 of another color, and 13 of another color. At this point 39 cards have been selected and we have accounted for three of the four colors. Next, to ensure that we have 3 cards selected of EACH color, we would select 3 cards of the final color.

Thus, the total number of cards that must be selected to ensure at least 3 cards of each color is

13 + 13 + 13 + 3 = 42.

Answer: C
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