Search for a tool
Binomial Coefficient

Tool to calculate the values of the binomial coefficient (combination choose operator) used for the development of the binomial but also for probabilities and counting.

Results

Binomial Coefficient -

Tag(s) : Combinatorics

dCode and you

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!
You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!


Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Binomial Coefficient tool. Thank you.

Binomial Coefficient

Sponsored ads

Binomial Coefficient Calculator

Combination of k choose n \( n \choose k \) or \( C_{n}^{k} \)



Tool to calculate the values of the binomial coefficient (combination choose operator) used for the development of the binomial but also for probabilities and counting.

Answers to Questions

What is the binomial coefficient? (Definition)

The binomial coefficient is noted \({n \choose k} \) or \( C_{n}^{k} \) and is defined by the formula $$ {n \choose k} = \frac{n!}{k!(n-k)!} $$

With \( n! \) the factorial of n.

How to calculat a binomial coefficient?

The binomial coefficient uses factorial functions whose values are simplified:

Example: \( {10 \choose 6} = \frac{10!}{6!4!} = \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1 \times 4 \times 3 \times 2 \times 1} = \frac{10 \times 9 \times 8 \times 7 }{4 \times 3 \times 2 \times 1} = \frac{5040}{24} = 210 \)

Why is so called the coefficient binomial?

The values of the binomial coefficient appear in the development of the Newton binomial:

$$ (a+b)^{n}=\sum_{k=0}^{n}{n \choose k}a^{{n-k}}b^{k} $$

Example: $$ (x+y)^{4} = x^4 + {4 \choose 1} x^3 y + {4 \choose 2} x^2 y^2 + {4 \choose 1} x y^3 + y^4 = x^4 + 4 x^3 y + 6 x^2 y^2 + 4 x y^3 + y^4 $$

What are binomial coefficient properties?

The folowing formulas can be useful:

$$ {n \choose k} = {n \choose n-k} $$

$$ {n \choose k} + {n \choose k+1} = {n+1 \choose k+1} $$

$$ {n \choose k} = {\frac{n}{k}}{n-1 \choose k-1} $$

When to use the binomial coefficient?

The binomial coefficient is used primarily in count and probability calculations. This is the basis for calculating the number of combinations of k elements out of n.

Example: The number of lotto combinations is 5 out of 49 ie \( {49 \choose 5} = 1906884 \) possible combinations.

Ask a new question

Source code

dCode retains ownership of the source code of the script Binomial Coefficient online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. So if you need to download the online Binomial Coefficient script for offline use, check contact page !

Questions / Comments


Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Binomial Coefficient tool. Thank you.


Source : https://www.dcode.fr/binomial-coefficient
© 2018 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode
Feedback