In a poker hand consisting of 5 cards, find the

dailinoyf

dailinoyf

Answered question

2021-12-03

In a poker hand consisting of 5 cards, find the probability of holding 3 aces.

Answer & Explanation

Ourst1977

Ourst1977

Beginner2021-12-04Added 21 answers

A poker hand consists of 5 cards (among which we need to have 3 aces).
In the standard 52-card deck, there are 4 aces, and we must select 3 of them.In order to calculate the number of ways of choosing 3 out of 4 aces, we need to use combinations (because the order is not important). So, we can choose 3 out of 4 aces in
(43)=4!3!(43)!=4 ways
We must now select 2 cards from the remaining 48 cards. (52 cards minus 4 aces). The number of ways to choose these 2 cards among 48 cards is
(482)=48!2!(482)!=48472=22562=1128 ways
If the first operation can be performed in 4 ways (the number of ways to choose 3 out of 4 aces), and for each of these ways the second operation can be performed in 1128 ways (the number of ways of choosing the remaining 2 cards), then these 2 operations can be performed together in
4*1128=4512 ways
So, there are 4512 ways to choose 3 aces in a poker hand.
There are 52 cards in total, and there are ways to select 5 of them.
525=52!5!(525)!=52515049484754321=2598960 ways
So, there are 2598960 ways for a poker hand.
Hence, the probability of choosing 3 aces in a poker hand is
P=The number of ways to choose 3 caces in a poker hand The number of ways to choose a poker hand =45122598960=0.00174
Result:
0.00174

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?