Mathematics Calculator

Equation

$${ }^a C_b={ }_a C_b=\left(\begin{array}{l}a \\b\end{array}\right)$$

$$\left(\begin{array}{l}a \\ b\end{array}\right)=\frac{a !}{b !(a-b) !}$$

Inputs

$a$ (total objects):

$b$ (sample taken):

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Result

$$ \left(\begin{array}{l}1 \\1\end{array}\right) = 1$$

Extra Analysis

$$\left(\begin{array}{l}1 \\ 1\end{array}\right)=\frac{1 !}{1 !(1-1) !}=\frac{1 !}{1 !(0) !}$$

$$=\frac{1}{(1)(1)}=\frac{1}{1}=1$$

Documentation

Combinations & Choose Formula

Basic Definition

The "choose" formula, sometimes referred to as the "binomial coefficient" is a mathematical function used to determine how many different ways there are to select a particular number of items from a bigger set, regardless of the order in which they are chosen.

Uses & Applications

To answer issues involving combinations, the "choose" formula is utilised in several disciplines, including probability, combinatorics, and statistics. The "choose" formula can be used in the following frequent situations:

a) Combinations

Counting all possible methods to choose "a" components out of a group of "b" elements without taking into account their order. Consider how many different options there are to select two winners from a group of ten competitors.

b) Probability

The "choose" formula in probability theory is used to determine the likelihood of various outcomes, particularly when the order of occurrences is unimportant.

c) Pascal's Triangle

The Pascal's Triangle, which has each entry equal to the sum of the two entries immediately above it, is a triangular form that can be used to represent the binomial coefficients. There are several uses for Pascal's Triangle, including the expansion of binomial equations and the resolution of specific probability issues.

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