Five cards are dealt from a standard 52-card deck.

(a) What is the probability that we draw 1 ace, 1 two, 1 three, 1 four, and 1 five (this is one way to get a "straight")?

(b) What is the probability that we draw any straight (including "straight flush" and "royal straight flush" hands)?

Guest Feb 13, 2020

#1**+1 **

(a) What is the probability that we draw 1 ace, 1 two, 1 three, 1 four, and 1 five (this is one way to get a "straight")?

In each case we want to select 1 of 4 cards from each of the specified ranks = [ C(4,1)]^5 = 4^5

And the total hands = C(52,5)

So.....the probability is just

4^5 / C(52,5) ≈ .000394 = .0394%

Note that these hands include the possibility of a straight flush ....

CPhill Feb 13, 2020

#2**+1 **

(b) What is the probability that we draw any straight (including "straight flush" and "royal straight flush" hands)?

This is similar to the last one

If we let the ace be the lowest or highest card in the straight.....we have 10 possible straights within the ranks :

A-2-3-4-5

2-3-4-5-6

......

10-J-Q-K-A

So the probability is just

C(10,1) * C(4,1)/ C(52,5) ≈ : .00394 = .394%

CPhill Feb 13, 2020