Meaning of notation with two letters inside of parentheses [binomial coefficient]

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Solution 1

$n\choose{k}$ is a 'binomial coefficient'. Sometimes read '$n$ choose $k$. It represents the number of ways of choosing $k$ items from $n$ distinct items where the order of choice is unimportant.

The value is ${{n}\choose {k}}=\frac{n!}{k!(n-k)!}$

$n$ and $k$ are nonnegative integers with $k\le n$.

Solution 2

Binomial coefficients. Relevant here is that:

$\begin{align} \sum_{0 \le k \le n} \binom{n}{k} a^k b^{n - k} = (a + b)^n \end{align}$

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Giteshwar Mali
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Giteshwar Mali

Updated on August 01, 2022

Comments

  • Giteshwar Mali
    Giteshwar Mali over 1 year

    What does the notation in the red box mean?

    $$\Huge e^{\displaystyle \large \sum_{k=0}^n \bbox[2px,border:2px solid red]{\color{black} { {n \choose k}}}~\omega^k}$$

  • Will R
    Will R over 7 years
    And so the exponent in the question is $(1+\omega)^{n}.$