# What is the probability of getting 2 ace cards?

Table of Contents

## What is the probability of getting 2 ace cards?

3/51

The chance of drawing one of the four aces from a standard deck of 52 cards is 4/52; but the chance of drawing a second ace is only 3/51, because after we drew the first ace, there were only three aces among the remaining 51 cards. Thus, the chance of drawing an ace on each of two draws is 4/52 × 3/51, or 1/221.

**What is the probability that a 5 card poker hand has at least one ace?**

This probability is (485)(525), for we have 48 choose 5 possible hands with no aces. Then the solution to the problem – that is, the probability of at least one ace appearing in a 5-card hand – is one minus the complement: 1−(485)(525).

### How many different five card hands have all five cards of a single suit?

There are 2,598,960 different combinations of five card poker hands. That is 52*51*50*49*48 divided by 5*4*3*2. Four of those combinations are Royal Flushes. 10,JQKA all of the same suit.

**How many five card poker hands consist of two aces two kings and a card of a different denomination?**

(b) How many poker hands consist of 2 Aces, 2 Kings and a card of a different denomination? You can pick the 2 aces, 2 kings in C(4,2) · C(4,2) = 6 · 6 = 36 ways. You can pick the remaining card in any of 52 − 8 = 44 ways so the answer is 36 · 44 = 1,584.

#### What is the probability of getting a 5-card poker hand?

There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million).

**How many Queens choose 2 in a five-card poker hand?**

There are 4 queens choose 2. There are 4 aces choose 2, and from the remaining 52 − 4 − 4 = 52 − 8 = 44 cards choose 1 to make a five-card poker hand. Pretty bloody low, I’d guess!

## What is the probability of all 5 cards from the same suit?

The probability is 0.003940. IF YOU MEAN TO EXCLUDE STRAIGHT FLUSHES AND ROYAL FLUSHES (SEE BELOW), the number of such hands is 10*[4-choose-1]^5 – 36 – 4 = 10200, with probability 0.00392465 A FLUSH Here all 5 cards are from the same suit (they may also be a straight). The number of such hands is (4-choose-1)* (13-choose-5).

**What is the probability of 36 hands in chess?**

The number of such hands is 4*10, and the probability is 0.0000153908. IF YOU MEAN TO EXCLUDE ROYAL FLUSHES, SUBTRACT 4 (SEE THE NEXT TYPE OF HAND): the number of hands would then be 4*10-4 = 36, with probability approximately 0.0000138517.