# factorial

1. ### Factorial proof

Hi all I've got a feeling this is a really simple question but I can't see it. Explain why p divides (2p-1)! Thanks, Alex
2. ### Hexadecimal and factorial question

Hello all, I am trying to find the last hexadecimal digit of a series of large factorials, but I'll start with 990! + 991! +...+1000!. I am trying to find the last hex digit of a larger sum than this, but I think all I need is a push in the right direction, because right now I am lost. Where...
3. ### poisson distribution

Hi I'm working on this problem. At a given time the number of households connected to the internet is a poisson random variable with mean=50. suppose the transmission rate available for the household is 20 mega bits per second. Find the probability of the distribution of the transmission rate...
4. ### Factorial / Circular Permutation Exam Question

Hi all, I recently had the following question on an exam: A dinner party is attended by four men and four women. How many unique ways can the eight people sit around the table? How many unique ways can the people sit around the table with men and women alternating seats? I answered since...
5. ### Factorial

10!/6!4! How is that 210?
6. ### Limit: Sum to infinity of reciprocals of factorials with alternating sign

Hello, I'm a bit stuck on this and would value your help please. I know that the sum to infinity of the reciprocals of factorials is e. But what if they have alternating sign, e.g. 1/1! - 1/2! + 1/3! + 1/4! - ... I have found the answer: identity (9) at...
7. ### likely simple probability questions

Hi All, New to probability and not great at it. I have two questions, and I'm looking for an explanation of how they can be solved numerically/using factorials. Both involve coins. First - if you flip a fair coin 8 times, what is the probability of getting 3 tails in a row? Second - if you...
8. ### 'Weird' Factorial Series

Hello, I am given the series\sum_{n=1}^{\infty} \frac{1\cdot3\cdot5\cdot...\cdot(2n-1)}{2\cdot5\cdot8\cdot...\cdot(3n-1)} and I am asked to determine whether it converges or diverges. The problem is that I can't come up with equation representing the series above, to me it looks like a modified...
9. ### Finding the Limit of a factorial Function

Hello, I have run across a function that uses factorials and I want to determine if it converges or diverges as 'n' approaches infinity. For example: lim_{n\to\infty} \frac{(2n+1)!}{(2n-1)!} = ? lim_{n\to\infty} \frac{n!}{2^n} = ? Any help is appreciated. -Sakon
10. ### Factorial

I tried inputing the factorial of 500 divided by 8 into my ti-84 plus graphing calculator and it gave me an error. Is it possible to find its value?
11. ### Probability question

Hi everyone, it's been a while since I've taken a basic probability class and I have a question about what I believe is conditional probability without replacement. The question is as follows: A group of children are going into a classroom with N adjacent chairs. Children walk into the room...
12. ### Urgent factorial binomial expansion

Find the coefficiants of x^5 in the expansion of (1+2x)^9 im struggling how to work out r? thanks
13. ### Factorial

Can someone explain how I solve the following factorial question? ((2-n)! + (n-2)!)/(3! + 0!) = 2/7 I don't get the (2-n)!+ (n-2)! part. How can I simplify that part?
14. ### Simplify Factorial Fraction

Simplify (2n)! divided by (2n+1)! The answer is 1/(2n+2)(2n+1). Can someone break it down for me step by step? How is this done?
15. ### evaluating an infinite sequence with a factorial

if I evaluate -2(n!)/(n^n) how can I tell if it's divergent or not? How would I take the limit at infinity?
16. ### Representation of a given polynomial in factorial notation

Hi, Represent f(x)=$2x^4 -12x^3 +24x^2 - 30x +9$ and its successive differences in factorial notation Solution:Let f(x) =$2x^4 - 12x^3 +24x^2 -30x +9$ =$2x^{(2)} +bx^{(3)} +cx^{(2)} +dx +9$ =2x(x-1)(x-2)(x-3) +bx(x-1)(x-2) +cx(x-1) +dx +9 where b,c and d are...
17. ### Factorial problem

I stumbled across this problem online, and was wondering how to go about solving it. \frac{((5000!)!)!}{(400!)!} It seems like the answer would be incredibly large.
18. ### Factorial

So here goes my problem. I am not allowed a calculator through this problem... 4! = 4 x 3 x 2 x 1 5! = 5 x 4 x 3 x 2 x 1 etc How many zeros are there at the end of 50! ? It would take me hours to do 50! = 50 x 49 x....x 1 by hand so how can I show the number of zeros at the end of 50...
19. ### Gamma function and factorial

Hi members, gamma(n+1)=n! Now I have an expression gamma (2(n+3/2))=gamma (2n+1) What is the factorial notation for this???
20. ### Help with factorial limit

Okays so, I have the limit as n-> infinity: (20n!)/((n+1)!) My first thought is that you would divided all terms by n, basically making the limit = 20!/1!, which is just 20!... but I don't think that this is correct. What do you guys think? Thanks.