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Questions tagged [binomial-coefficients]

It is the coefficient of the `x^k` term in the polynomial expansion of the binomial power `(1 + x)^n` which is `(n!)/((n-k)!*k!)`.

It is the coefficient of the x^k term in the polynomial expansion of the binomial power (1 + x)^n which is (n!)/((n-k)!*k!).

This family of numbers also arises in many areas of mathematics other than algebra, notably in combinatorics. For any set containing n elements, the number of distinct k-element subsets of it that can be formed (the k-combinations of its elements) is given by the binomial coefficient C(n, k). Therefore C(n, k) is often read as "n choose k".

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Combs on a large set doesn't compute Haskell

I'm writing a combs function in haskell what it needs to do is, when I provide it with a deck of cards, give me every combination of hands possible from that deck of size x This is the relevant code combs :: Int -> [a] -> [[a]] combs 0 _ = [[…
LordofTurtles
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Explanation for calculating ncr

I was reading the possible efficient methods for calculating ncr when I came across this post. Which is better way to calculate nCr The second answer given here, an I'm not able to understand that. The code is: long long combi(int n,int k) { …
chan chong
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How to compute sum of evenly spaced binomial coefficients

How to find sum of evenly spaced Binomial coefficients modulo M? ie. (nCa + nCa+r + nCa+2r + nCa+3r + ... + nCa+kr) % M = ? given: 0 <= a < r, a + kr <= n < a + (k+1)r, n < 105, r < 100 My first attempt was: int res = 0; int mod=1000000009; for…
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Binomial coefficient with large integers in C

Some time ago I created a big integer library, to compute the factorial of large integers (up to five million) using FFT and binary splitting. Now I need to compute the binomial coefficent (n! /(k! *(n-k)!)) with big integers (something like n=10000…
feazzu
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Polynomial expansion: Separating polynomial coefficients and x's

I want to automatically calculate expansions of polynomials where there are variables (x1,x2,...) as well as coefficients (c1,c2, ...). My goal is to calculate p(1)*(c1*x1+c2*x2+...)^n+ ... + p(n)*(c1*x1+c2*x2+...)^n . As you can notice the…
jkt
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How to make the plus sign show for a variable in python

I am currently working on a program in Python that will factor trinomial equations into binomial equations. However, the problem is that whenever I calculate the binomials, if it is positive then the + sign will not show up. For example, when I…
Domecraft
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How to do binomial distribution in python where trial probabilities are unequal

I know how to do a standard binomial distribution in python where probabilities of each trial is the same. My question is what to do if the trial probabilities change each time. I'm drafting up an algorithm based on the paper below but thought I…
dotdotdog
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ncr in c (combinations)

I m trying to calculate ncr(combinations) in c using dp. But it is failing with n=70. Can anyone help? unsigned long long ncr( int n , int r) { unsigned long long c[1001]; int i=1; c[0]=1; for(i=1; i<=r; i++) c[i]= ((unsigned long long)…
bhavneet
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binomial coefficient

I have a code which calculate binomial coefficient, but when number is bigger then 20, it start to calculate wrong, where is the problem? Thanks #include using namespace std; long int bin(long int x) { if(x==0) return 1; …
user1751550
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Divisibilty of binomial coefficient(nCk) with prime number(P) for large n and k

In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. nCk denotes the number of ways of choosing k objects from n different objects. However when n and k are too large, we often…
user1514387
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Does a/b mod m = (a mod m)/(b mod m)?

Does a/b mod m = (a mod m)/(b mod m)? I am trying to find nCr mod m for very large numbers. If a/b mod m = (a mod m)/(b mod m) then think I will have solved my problem. It is for Project Euler. I am using the nCr formula using factorials.
Andrew Koroluk
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matlab command: stock price in the binomial model

can someone kindly help me with the binomial model (in the context of stocks): on the page 36 [here] (https://www.mathworks.com/help/releases/R2021a/pdf_doc/finance/fintbx.pdf) in the OptionPrice matrix there are always 3 numbers non-zero in the 4,5…
user2925716
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Binominal coefficient in python

so I was wondering how i could get around this problem where i have this code #defining a function that computes the factorial of an integer def fac(b): if b==1: return 1 else: return b * fac(b-1) #takes two integers and does the…
LAXEN OSUND
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Binomial coefficients on cartesian form python program

I need help to construct a python program! Ok so I have to write a code that solves binomial coefficients with the following formula. What it basically says is the same as the sum from j to i, just that it multiplicates. This is a generalization of…
ROLLIN40SCRIPS
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Adding values to a vector until its sum is in a certain range

I'm trying to write a simple script in R to output a vector of binomially distributed values such that the sum of the values is in a given range. I know I will need to use the command rbinom to draw values from the binomial distribution but I can't…
Tsing Shi Tao
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