# How many different 5 card hands with only black cards are possible?

## How many different 5 card hands with only black cards are possible?

To calculate how many 5 card hands contain at least one black card it is easier to calculate how manny hands have no black cards and the subtract this from the total number of 5 card hands. Number of hands containing at least one black card=2,598,960-67,780=2,531,180.

How many different 3 card hands can be dealt from a deck of 52 cards your answer is?

Within each of the three suits drawn, there are 13C1 = 13 possible cards which could be drawn. Therefore, the answer is 4 * 13 * 13 * 13 = 8,788 possible different three-card hands containing three different suits which can be drawn. A standard deck of cards has 52 different cards.

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### How many 5 card hands have exactly 3 hearts?

How many possible 5-card hands from a deck of 52 cards are there that consists of 3 hearts and a three-of-a-kind? C(3,2) = number of ways to choose 2 cards from the remaining suits to complete the three-of-a-kind. So, in total, we have: C(13,3) * C(3,1) * C(3,2) possible hands.

How many different 5 card hands are possible?

2,598,960 distinct
Probability of a Full House First, count the number of five-card hands that can be dealt from a standard deck of 52 cards. We did this in the previous section, and found that there are 2,598,960 distinct poker hands. Next, count the number of ways that five cards can be dealt to produce a full house.

## How many 5 card poker hands have 3 red cards and 2 black cards?

We want exactly 3 red cards and 2 black cards. \displaystyle \text{We want exactly 3 red cards and 2 black cards.} We want exactly 3 red cards and 2 black cards. Therefore, there are: 2600 ⋅ 325 = 845 , ⁣ 000 ways to get exactly 3 red cards.

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How many 5 card hands will consist of exactly 3 Kings and 2 Queens?

24 five-card hands
24 five-card hands contain exactly 3 kings and 2 aces.

### How many 5 card hands consist only of hearts?

Yes, there are 52C5 = 52! / (47! 5!) = 2,598,960 five card hands. There are 13C5 = 1287 hands that consist entirely of hearts; that’s the difference between 2,598,960 and 2,597,673.

How many red cards and black cards are in the deck?

(a) There are 26 red cards and 26 black cards in the deck. . . . . W e w a n t e x a c t l y 3 r e d c a r d s a n d 2 b l a c k c a r d s.

## How many hearts are there in a deck of cards?

Red (26 cards) and Black (26 cards). The red cards are further divided into diamonds♦️ (13 cards) and hearts♥️ (13 cards). The black cards are further divided into clubs ♣️ (13 cards) and spades ♠️ (13 cards).

What is half of a deck of 52 playing cards?

A standard deck contains 52 playing cards, and half the deck is black, which gives us: $52 \imes \\frac{1}{2} = \\frac{52}{2} = 26$ black cards.

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### How many face cards are in a deck of cards?

\\displaystyle ext {The 12 face cards are removed from a deck.} The 12 face cards are removed from a deck. F r o m t h e s e 1 2 f a c e c a r d s, 4 a r e c h o s e n. \\displaystyle ext {From these 12 face cards, 4 are chosen.} From these 12 face cards, 4 are chosen.