# Thread: What formulas do I need?

1. ## What formulas do I need?

So I am revising for my maths test resit cos I suck lol but anyway I have this question

Q1. A suit of playing cards has 13 cards, Ace through to King. What is the probability of the deck containing one suit being in order: A23456789TJQK after an unbiased shuffle? Inlude your reasoning.

I know it's 13! but how would I show this answer using a formula? I think it's nCk but I'm not sure, it's worth 5% so I need to include something in there.

2. ## Re: What formulas do I need?

Originally Posted by uperkurk
So I am revising for my maths test resit cos I suck lol but anyway I have this question
Q1. A suit of playing cards has 13 cards, Ace through to King. What is the probability of the deck containing one suit being in order: A23456789TJQK after an unbiased shuffle? Inlude your reasoning.
I know it's 13! but how would I show this answer using a formula? I think it's nCk but I'm not sure, it's worth 5% so I need to include something in there.
The answer depends on how one reads the question. If it means that the suit is one block is that order then $\frac{40!}{52!}$.

On other hand it it means the suit can be spread out but in that order then $\frac{\binom{52}{13}\cdot 39!}{52!}$.

3. ## Re: What formulas do I need?

Originally Posted by uperkurk
So I am revising for my maths test resit cos I suck lol but anyway I have this question

Q1. A suit of playing cards has 13 cards, Ace through to King. What is the probability of the deck containing one suit being in order: A23456789TJQK after an unbiased shuffle? Inlude your reasoning.

I know it's 13!
I'm sorry to hear that. Do you not know that a probability is always between 0 and 1?

but how would I show this answer using a formula? I think it's nCk but I'm not sure, it's worth 5% so I need to include something in there.
I think your problem is that you have no idea what the problem is asking. 13! is nowhere near the correct answer.

4. ## Re: What formulas do I need?

Well that's frustrating lol... you're right I don't understand half the questions i'm given, I really struggle with maths but I thought the question meant what are the chances, if you kept shuffling the deck over and over that you'd end up with 1 of the suits in full order. Please explain to question so I get what it means thanks.

5. ## Re: What formulas do I need?

Originally Posted by Plato
$\frac{\binom{52}{13}\cdot 39!}{52!}$.
That is the correct one because it asks in order, A23456789TJQK but can you read this out to me? How do I even read your answer in english.

6. ## Re: What formulas do I need?

Originally Posted by uperkurk
That is the correct one because it asks in order, A23456789TJQK but can you read this out to me? How do I even read your answer in english.
Well the final answer is $\frac{1}{13!}$. WHY?
Because $\frac{52!}{13!}$ is the number of ways to arrange 52 cards so that one particular suit is in ascending order ace to king. If we want the probability we divide by $52!$.

7. ## Re: What formulas do I need?

oh I understand it now.... so there is just as much chance that lets say A2K36579Q48J appearing as there is A23456789JQK, I need to ignore the whole suit part of the question and just think of that as 1 combination, and there are 13! different combinations for that suit to be arranged?

8. ## Re: What formulas do I need?

Originally Posted by uperkurk
oh I understand it now.... so there is just as much chance that lets say A2K36579Q48J appearing as there is A23456789JQK, I need to ignore the whole suit part of the question and just think of that as 1 combination, and there are 13! different combinations for that suit to be arranged?
Actually that is a very good way to look at this particular question.