How many 5-card combinations are there in a single deck of cards?
How many in two decks?
Please show working.
(This amn’t anyone’s homework, but I was too tired to work it out myself. I see that Mr Turing is back; please bump it for him if no-one else cares.)
Isn’t it just 5^52=2.22044046e+36? ie a fair few.
Wait, it depends on whether the order that the cards is important or not?
If its not important, it would be 52 × 51 × 5 = 13,260.
I think… But I don’t know. I not good at maths. Shouldn’t have said anything. Forget i was here, please. Sorry :)
1 deck —> nCr 52 5 = 2,598,960
2 deck —> nCr 104 5 = 91,962,520
52!/5!(52-5)!
= 52!/(5! *47!)
err, get out mathcad…2598960
For the two packs it will be 104!/ 5!(104-5)! = 104!/(5!*99!) = 91962520
…depends on whether the order that the cards are drawn is significant or not…. I meant to say.
Ta. And no, the order doesn’t matter.
(Knew it was something simple, that I used to know.)
I, of course, have the only correct answer, as the question asked “to show workings”.
diddly gets half marks :)
OCDC said:
Ta. And no, the order doesn’t matter.(Knew it was something simple, that I used to know.)
Combination —> order doesn’t matter
Permertation —> order does matter
OCDC said:
Ta. And no, the order doesn’t matter.(Knew it was something simple, that I used to know.)
Combination —> order doesn’t matter
Permertation —> order does matter
sibeen said:
I, of course, have the only correct answer, as the question asked “to show workings”.diddly gets half marks :)
Dude.. I showed how to work a calculator to get the answer…
diddly-squat said:
*permutation
OCDC said:
Ta. And no, the order doesn’t matter.(Knew it was something simple, that I used to know.)
Combination —> order doesn’t matter
Permertation —> order does matter
Diddly squat and sibeen agree with each other, and seem to know what they are talking about.
I, on the other hand, seem to have got everything wrong.
OCDC said:
Ta. And no, the order doesn’t matter.(Knew it was something simple, that I used to know.)
I remember learning this stuff in yr 11. Too bad I don’t remember what any of it was…
>Dude.. I showed how to work a calculator to get the answer…
Yes, but I showed an equation that can easily be worked out without recourse to electronic calculating machines :)
Angus Prune said:
OCDC said:
Ta. And no, the order doesn’t matter.(Knew it was something simple, that I used to know.)
I remember learning this stuff in yr 11. Too bad I don’t remember what any of it was…
diddly-squat said:
1 deck —> nCr 52 5 = 2,598,960
2 deck —> nCr 104 5 = 91,962,520
Just out of interest, what does 5^52 calculate? Anything? Or is it just a random assembly of numbers and operations with no significance to decks of cards and combinations of cards?
OCDC said:
Angus Prune said:
OCDC said:
Ta. And no, the order doesn’t matter.(Knew it was something simple, that I used to know.)
I remember learning this stuff in yr 11. Too bad I don’t remember what any of it was…
I learnt it in year 8 and tutored it for goodness knows how many years after, which makes it even more embarrassing.
Yeah but that was like a million years ago
5^52 = 2.22*10^36
It just means 5 × 5 × 5 …with 52 fives.
esselte said:
diddly-squat said:1 deck —> nCr 52 5 = 2,598,960
2 deck —> nCr 104 5 = 91,962,520
Just out of interest, what does 5^52 calculate? Anything? Or is it just a random assembly of numbers and operations with no significance to decks of cards and combinations of cards?
5^52 simply equals 5 × 5 × 5 × 5 …. 52 times over
5^52 = 2.22 × 10^36
So no significance to the question? It’s not, like, the number of possible combinations in 5 decks of cards or anything like that?
Lucky you got that last one in. I was about to give you half marks again.
Nil, esselte.
sibeen said:
Lucky you got that last one in. I was about to give you half marks again.
diddly 1.5
sibeen 1
sibeen said:
Nil, esselte.
Hah. My parents paid for a private school education for me. I guess the jokes on them :)
esselte said:
So no significance to the question? It’s not, like, the number of possible combinations in 5 decks of cards or anything like that?
If I had 52 decks of 5 cards, and drew one card from each, the number of possible hands would be 5^52.
Aha. So My answer was actually correct, and it’s just that OCDC asked the wrong question.
I feel much better now. Thanks Wocky!
esselte said:
Aha. So My answer was actually correct, and it’s just that OCDC asked the wrong question.I feel much better now. Thanks Wocky!
I aim to please (:
and the two deck answer only holds if you assume that all cards are unique, that is, there is a way to distinguish between the 5 hearts in one deck and the 5 hearts in the other.
Good point, diddly. I didn’t consider that.
esselte said:
My parents paid for a private school education for me. I guess the jokes on them :)
Were apostrophes an optional extra, by any chance?
;-)
Rule 303 said:
esselte said:My parents paid for a private school education for me. I guess the jokes on them :)
Were apostrophes an optional extra, by any chance?
;-)
It was an Anglican school. We were too busy learning about God to be bothered by such minutiae.
diddly-squat said:
and the two deck answer only holds if you assume that all cards are unique, that is, there is a way to distinguish between the 5 hearts in one deck and the 5 hearts in the other.
Indeed. And if we don’t care which deck a card comes from, the answer is much smaller:
52C5 + 4×52C4 + 3×52C3 = 3748160.
That’s 52C5 combinations with no duplicated cards,
plus 4×52C4 combinations with one duplicated card,
and 3×52C3 with two duplicated cards.
Ta.
I just ran a little Python program to confirm my formula. It took 17 minutes to count all the combinations. (But I did check it before I posted using several smaller deck sizes).