Answer to Question #270883 in Discrete Mathematics for kd bhai

Question

How many cards must be selected from a standard deck of 52 cards to guarantee that at least three

cards of the same suit are chosen? How many must be selected to guarantee that at least 3 hearts

selected?

Answer 1

1) If 8 cards are chosen, it is possible that there are 2 cards of each suit.

So, it must be 9 cards to guarantee that at least three cards of the same suit are chosen.

2) If 13+13+13=39 cards are chosen, it is possible that there are no heart cards are selected.

So, it must be 39+3=42 cards to guarantee that at least 3 hearts are selected.