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

Question

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

A. 40
B. 41
C. 42
D. 43
E. 44

LenaA · Accepted Answer

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.

LenaA · Answer

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.

konayuki · Answer

42 is right... but I do not get it.

Help me with the logic!

GMATinsight · Answer

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

azhrhasan · Answer

42.

worst case + 1

(13+13+13+2)+1

akadiyan · Answer

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

ScottTargetTestPrep · Answer

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

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