## A single PAIR

This the hand through the pattern AABCD,where A, B, C and D room from the distinct "kinds" that cards: aces,twos, threes, tens, jacks, queens, and kings (there room 13 kinds,and four of each kind, in the traditional 52 map deck). The number ofsuch hand is (13-choose-1)*(4-choose-2)*(12-choose-3)*<(4-choose-1)>^3.If all hands are equally likely, the probability of a solitary pair isobtained by dividing by (52-choose-5). This probability is 0.422569.

You are watching: How many 5 card hands are possible

## TWO PAIR

This hand has the pattern AABBC whereby A, B,and C are from distinct kinds. The variety of such hands is(13-choose-2)(4-choose-2)(4-choose-2)(11-choose-1)(4-choose-1).After splitting by (52-choose-5), the probability is 0.047539.

## A TRIPLE

This hand has the pattern AAABC whereby A, B,and C are from distinctive kinds. The variety of such hands is(13-choose-1)(4-choose-3)(12-choose-2)<4-choose-1>^2. The probabilityis 0.021128.

See more: Why Did Thomas Jefferson Wear A Wig, Hamilton And The History Of The Wig

## A complete HOUSE

This hand has actually the pattern AAABB whereA and B space from unique kinds. The number of such hands is(13-choose-1)(4-choose-3)(12-choose-1)(4-choose-2). The probabilityis 0.001441.

## four OF A sort

This hand has the pattern AAAAB whereA and also B room from distinctive kinds. The number of such hand is(13-choose-1)(4-choose-4)(12-choose-1)(4-choose-1). The probabilityis 0.000240.

## A right

This is 5 cards in a sequence (e.g.,4,5,6,7,8), v aces enabled to be either 1 or 13 (low or high) andwith the cards allowed to it is in of the exact same suit (e.g., all hearts) orfrom some various suits. The variety of such hands is 10*<4-choose-1>^5.The probability is 0.003940. IF YOU typical TO EXCLUDE straight FLUSHESAND imperial FLUSHES (SEE BELOW), the number of such hand is 10*<4-choose-1>^5 - 36 - 4 = 10200, v probability 0.00392465

## A do the washing up

right here all 5 cards are from the exact same suit(they may likewise be a straight). The number of such hand is (4-choose-1)*(13-choose-5). The probability is approximately 0.00198079. IF YOU typical TO EXCLUDE straight FLUSHES, SUBTRACT 4*10 (SEE THE following TYPEOF HAND): the variety of hands would certainly then it is in (4-choose-1)*(13-choose-5)-4*10,with probability around 0.0019654.

## A directly FLUSH

all 5 cards room from the exact same suitand they form a right (they may also be a imperial flush). The variety of such hand is 4*10, and also theprobability is 0.0000153908. IF YOU average TO EXCLUDE imperial FLUSHES, SUBTRACT 4(SEE THE NEXT type OF HAND): the number of hands would certainly then be 4*10-4 = 36, with probability approximately0.0000138517.

## A imperial FLUSH

This consists of the ten, jack, queen,king, and also ace that one suit. Over there are 4 such hands. The probabilityis 0.00000153908.

## none OF THE over

We have actually to select 5 distinctive kinds(13-choose-5) yet exclude any type of straights (subtract 10). We can have anypattern of suits except the 4 patterns where every 5 cards have actually thesame suit: 4^5-4. The total variety of such hand is <(13-choose-5)-10>*(4^5-4). The probability is 0.501177.