With a standard 52 deck (13 types and 4 suites), what is the probability that a poker hand contains

Cooper Krause

Cooper Krause

Answered question

2022-05-21

With a standard 52 deck (13 types and 4 suites), what is the probability that a poker hand contains cards of five different types? A poker hand is a set of 5 cards.
The obvious answer is A / B where A is the number of poker hands that have 5 different types of cards and B is the total number of poker hands which is C(52,5).
Right now I think A = C(13,5) since there are 13 different types of cards I choose 5 from them but I am unsure if A = 4 * C(13,5) instead, where 4 is the different suites.

Answer & Explanation

stacan6t

stacan6t

Beginner2022-05-22Added 13 answers

After the first card, we are smiling. The probability we are still smiling after the second card is 48 51 for there are 3 cards that will stop the smile. Given that we were smiling after the second card, the probability that we are still smiling after the third card is 44 50 since we need to avoid the first two types. And so on. The required probability is therefore
48 51 44 50 40 49 36 48 .
Jaidyn Bush

Jaidyn Bush

Beginner2022-05-23Added 1 answers

There are ( 52 5 ) total ways of drawing 5 cards, where order doesn't matter, as you say. Then there are ( 13 5 ) ways to choose the five ranks (types) of your cards. But you now have to choose for each of the five cards which suit it is, and there are not one, but five such choices you have to make. So the answer is
( 13 5 ) 4 4 4 4 4 ( 52 5 )

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