📚 Binomial Coefficients

Counting problem++

Determine the number of ways to choose $r$ elements from $n$ without regard for order.

Theory:

The binomial coefficient, often written as $C(n,r)$ or $\left(\genfrac{}{}{0ex}{}{n}{r}\right)$, is:

$$C(n,r)=\frac{n!}{r!(n-r)!}$$

Used in binomial expansions like:

$$(x+y{)}^n=\sum _{r=0}^{n}C(n,r)x^{n-r}{y}^r$$

Where:

• $n$ : Total number of objects
• $r$ : Number of objects to choose