Question

A 5-card hand is dealt from a well-shuffled deck of 52 playing cards. What is the probability that the hand contains at least one card from each of the four suits?

Answer 1

Answer:

0.2637

Step-by-step explanation:

We see from the question that the 5-card hand contains all 4 suits as shown below;

Number of cards = 52

Number of suits = 4

For the favorable cases therefore, we will choose two cards from the suit in which two cards are drawn. Then we will proceed to choose one card from each of the other suits.

4 suits will divide into 52 cards to give = (52 / 4) = 13 cards

Hence, the required probability;

$= {\frac{4 *13c_2*13c_1*13c_1*13c_1}{52c_5}}\\= {\frac{2197}{8330}}\\= 0.2637$