Greatest Value of ${}^nC_r$

Greatest Value of ${}^nC_r$

## Formula

The greatest value among:

$${}^nC_0,{}^nC_1,{}^nC_2,\ldots,{}^nC_n$$

is:

$${}^nC_{\lfloor n/2\rfloor}$$

If $$n$$ is even, the greatest coefficient is:

$${}^nC_{n/2}$$

If $$n$$ is odd, there are two equal greatest coefficients:

$${}^nC_{(n-1)/2}={}^{n}C_{(n+1)/2}$$

## Usage

- Used to find the largest binomial coefficient without calculating every term.