Answer to Question #142648 in Discrete Mathematics for Amina

Question

a) 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? b) How many must be selected to guarantee that at least three hearts are selected?

Answer 1

$a)\text{According to the principle of the Dirichle box}$

$n= km+1,\text{where }m=4 \text{ number of suits, }$

$k+1\ge3\text{ number of cards of the same suit}$

$n- \text{total number of selected cards}$

$n = 2*4+1 =9$

$b)\text{Number of cards not containing the suit of hearts }3*13=39$

$\text{For a guaranteed selection of a set of cards containing 3 cards }$

$\text{ of the suit of hearts, you must select }39+3 =42$

Answer: a) 9 cards b) 42 cards