# binomial

1. ### Question related with Binomial Theorem

How can we find the index 'n' of the binomial \left ( \frac{x}{5}+\frac{2}{5} \right )^{n}, n\epsilon N if the 9th term of the expansion has numerically the greatest coefficient. Thx.
2. ### Binomial theorem

How can I prove the equation by using binomial theorem? Thanks.
3. ### binomial exp for non-integer power

the expansion of (1+x)^n where n is an irrational number. Is this state is true: (1+x)^n = 1 + nx +1/2 n(n-1) x^2 + ...... i.e is it right that (1+x)^root(3) = 1 + root(3)x + 1/2 root(3) ( root(3)-1)x^2 + .....
4. ### Binomial equations

Hello, I am new to the forum, so hello to everyone. I need some help with 2 equations that need to be proved. Thank you in advance.
5. ### divisiblity of a binomial coefficient

Hello, how to show the following?? : $C_{2^{m-1}}^{k}\times 2^k$ is divisible by $2^{m}$. with for any $k$ such that $2^{m-1}\geq k \geq 1$.
6. ### Binomial Expansion - The notation

Q1: nCr+1 - nCr-1 = n+1Cr-1 - n+1Cr Q2: nC3 = 5nC1 Q3: nC1+ nC2 = 3n I would like to know how to solve these questions with detail steps, thank you!! My answer on Q2 is 1 and Q3 is 4 but the model answer are 7 and 5 respectively.
7. ### why 2n above n (binomial) is, equal or less than, 4^n ?

i mean i know that 4^n = (1+1)^(2n) and 2n above n (binomial) is equals to 2n!/n!(2n-n)! but how do i put those in words to prove the equation (Title) ...? sorry i haven't seen any method in the formulas of how to write the binomial expression ...
8. ### The P.M.F. of Hypergeometric and Negative Binomial Distribution.

A forest contains 100 deer. 20 of them have a red tag and 80 of them are untagged. A researcher samples 30 random deer without replacement. Let X be the number of tagged deer in the sample. From the sample of 30 deer, she will keep picking deer with replacement until she picks the fourth tagged...
9. ### Question Discrete Math Binomial Theorem

Please could someone help me the way to approach this?
10. ### Question binomial theorem

Given 1/(1+cube root (x)) find its series using the binomial theorem. Use this series to approximate y at x = 1/2 and find the error between the real value and the approximated value for y at x = 1/2 (assuming n = 6). I was given a question similar to above which I have changed a bit as I...
11. ### Binomial Sum

Prove that \displaystyle \binom{n}{1}-\left(1+\frac{1}{2}\right)\binom{n}{2}+\left(1+ \frac{1}{2}+\frac{1}{3}\right)\binom{n}{3}+\cdots \cdots \cdots +(-1)^n\left(1+\frac{1}{2}+\frac{1}{3}+\cdots \cdots +\frac{1}{n}\right)=\frac{1}{n}
12. ### Binomial Distribution Probability

A toy manufacturing company tests the quality of the toys it manufactures. On a daily basis, 20 toys are taken at random for testing and to check that 95% meet the toy specification. The day's production will be accepted provided that no more than 2 toys fail to meet the specification standard...
13. ### Counting Prin. & Binomial T.

So, I'm trying to focus heavily on mastering this topic for my upcoming meet. This is a 5-point question, and I have yet to understand the process to get to the answer. Question: Find the number of positive integers less than 10,000 with all distinct digits. Any possible ideas? Also...
14. ### Binomial Expansion Help Needed!

I came across a question, which was: Find the coefficient of c^4d^11 in the expansion of (2c+5d)(c+d)^14. I can do it easily with the (c+d) bracket, but the (2c+5d) complicates it for me. Could someone help me out? Thanks a lot!
15. ### Maximum of a binomial

If X is a binomial random variable, for what value of theta is the probability b(x;n,theta) a maximum? In their notation theta is the probability of a success and n is the number of trials. I'm not sure where to start to be honest. For a given value of the parameters I could say the...
16. ### Binomial Distribution

Hi everyone. Second question for today. And this question doesn't have answer on my practice book. So I need help from members at this forum. Q. Between 1872 and 2000, stock prices rose in 74% of the years. Based on this information, and assuming a binomial distribution, what do you think is...
17. ### derive variance using binomial random variable

Hi if it helps I have just proved that E(X) of a binomial random variable is N*theta where R~Bin(N,theta) However I am unsure how to start variance proof.
18. ### Divisibility of a binomial coefficient

I want to proof, why \frac {\binom {2n}{n} - 2}{n} always returns an integer if n is a prime, but I don't know how.. You can write it like the following but I don't see a beginning for a proof...: \frac {\binom...
19. ### Expected Value and Variance of a Binomial Distribution

Hello, I search in google for proof Expected Value and Variance of a Binomial Distribution. But i can't understand well. Could you please proof E[X] and VAR[X] with more explain and simplify? Thanks :inlove:
20. ### Binomial distribution and Poisson help please Â£20 gift card for amazon

Hi guys really struggling understanding this. Using the formula and finding the probality im finding kina kind. Also how to write it in the calculator correctly. Please help if you have an understanding 7. A shopkeeper finds that 20% of the cartons containing 6 eggs he receives are...