Question

Five cards (a hand) are dealt from a randomly shuffled deck of cards. For those of you that are not familiar with playing cards: each card has a suit (hearts, spades, diamonds, clubs) and a symbol (aces, kings, queens, etc.). The deck contains a total of 52 cards, with 13 of each suit and 4 of each symbol. What is the probability that the hand contains a) all spades

Answer 1

Answer: 0.0004951

Step-by-step explanation:

Given

Five cards are from the deck

The total number of cards in the deck is 52

total spades card is $13$

We have to choose 5 cards out of 13, this can be done in

$\Rightarrow ^{13}C_5$

The probability of choosing 5 spade cards is

$\Rightarrow P=\dfrac{^{13}C_5}{^{52}C_5}\\\\\Rightarrow P=\dfrac{1287}{2598960}=0.0004951$