How many combinations of 3 playing cards exist?

1 Expert Answer

To answer a), we note that there 52 ways to choose the first card, 51 ways to choose the second card, and 50 ways to choose the third card, for a total of 52*51*50=132,600 ways.

How many combinations of 3 playing cards from a 52 card deck?

In how many ways can a three card be drawn from 52 playing cards? The first card can be drawn in 52 different ways, the second card in 51 ways and the third in 50 ways. Therefore, there are 52*51*50 ways of drawing three cards from the pack of 52 playing cards. There are 132600 ways are there.

How many combinations of playing cards exist?

There are 52 cards in each deck, meaning that the total possible combinations would equal 52! (52 factorial) which is equal to 8.06e+67.

How big is 52 factorial?

52! is approximately 8.0658e67. For an exact representation, view a factorial table or try a "new-school" calculator, one that understands long integers.

What is the probability of drawing a 3 card?

The probability of drawing a spade or a 3 from a well shuffled deck of 52 cards is 17/52.

Combinations of 52 cards (52 factorial)

What is the probability that 3 cards are drawn from a standard 52 card deck?

Three cards are drawn from a standard 52-card deck of cards without replacement. What's the probability that the third card drawn is a heart if the first two cards were also hearts? 11/50.

What is the probability of drawing a 3 from a standard deck of 52 cards?

The probability of randomly drawing from a sorted deck a 3 is 4/52 or 1/13. Without replacing the first card drawn the probability of drawing a 5 is 4/51. The probability of drawing a 3 and then a 5 is 1/13*4/51=0.0060.

Why is 52 factorial so special?

The number of possible ways to order a pack of 52 cards is '52! ' (“52 factorial”) which means multiplying 52 by 51 by 50… all the way down to 1. The number you get at the end is 8×10^67 (8 with 67 '0's after it), essentially meaning that a randomly shuffled deck has never been seen before and will never be seen again.

What is the largest possible factorial?

The last factorial is 170! “Did you know? The number 170 is the highest possible number you can calculate a factorial for? Any higher than 170, and the mathematical answer is infinity.” - visualfractions.com/calculator/fac…

How many combinations of 5 playing cards are there?

5! = 2598960 different ways to choose 5 cards from the available 52 cards.

How many combinations of 2 cards are there?

Essentials. There are 1326 distinct possible combinations of two hole cards from a standard 52-card deck in hold 'em, but since suits have no absolute value in this poker variant, many of these hands are identical in value before the flop.

How many combinations of three numbers are there?

There are 504 different 3-digit numbers which can be formed from numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 if no repetition is allowed. Note: We can also use the multiplication principle to answer this question.

How many combinations of 52 playing cards are there?

No one has or likely ever will hold the exact same arrangement of 52 cards as you did during that game. It seems unbelievable, but there are somewhere in the range of 8x10⁶⁷ ways to sort a deck of cards. That's an 8 followed by 67 zeros.

Are there more combinations of cards than atoms?

That's not even close! There are roughly eight-hundred-quadrillion times more ways to shuffle a deck of cards than atoms on Earth.

How many multiples of 3 cards are in a deck?

In a deck of 52 cards, for each suit, we have three cards with number 3, 6, 9 which are multiples of 3.

Why is 69 factorial special?

On many handheld scientific and graphing calculators, the highest factorial that can be calculated, due to memory limitations, is 69! or about 1.711224524×10⁹⁸.

Why is 69 the highest factorial?

That is because 70! is more than 10^100 , which the calculator cannot display, and hence 69! is the max value ie, 69 is the largest integer for which a standard calculator displays the factorial value.

Why is 170 the highest factorial?

170 is the largest integer for which its factorial can be stored in IEEE 754 double-precision floating-point format. This is probably why it is also the largest factorial that Google's built-in calculator will calculate, returning the answer as 170! = 7.25741562 × 10³⁰⁶.

How many zeros does 52 factorial have?

; that is, 1 followed by 68 zeros. Describing 52!

What is a fun fact about factorials?

Factorials are always integers because it's the result of multiplying integers together. Modern computers covert our everyday numbers into binary, using only 0s and 1s, before they do any calculation.

What is the probability that 3 of the cards will be black?

Therefore, the probability of drawing three black cards in a row is around 12% or 0.12 .

What is the probability 3 of spades?

Therefore, the probability of getting 3 spades is 0.0129.

What is the probability of drawing a black king and red queen?

AI Recommended Answer: The probability that the card is black king or a red queen is 1/52.