Tricky Min/Max Problem

[tarunjohri]

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

Please Explain the Solution.

[aaggar7]

Let the four colors be A,B,C,D.

and each (A,B,C,D) has 13 cards from (1 to 13).

To ensure we select 3 cards of each colour = 3 * 13 + 3 = 42 is the min number of cards to be selected.

A - 1 2 3 4 5 6 7 8 9 10 11 12 13
B - 1 2 3 4 5 6 7 8 9 10 11 12 13
C - 1 2 3 4 5 6 7 8 9 10 11 12 13
D - 1 2 3 4 5 6 7 8 9 10 11 12 13

[tarunjohri]

Thanks a lot for your explanation.

Let the four colors be A,B,C,D.

and each (A,B,C,D) has 13 cards from (1 to 13).

To ensure we select 3 cards of each colour = 3 * 13 + 3 = 42 is the min number of cards to be selected.

A - 1 2 3 4 5 6 7 8 9 10 11 12 13
B - 1 2 3 4 5 6 7 8 9 10 11 12 13
C - 1 2 3 4 5 6 7 8 9 10 11 12 13
D - 1 2 3 4 5 6 7 8 9 10 11 12 13