# Fungrim entry: 4e7120

${n \choose k} \le \frac{{n}^{n}}{{k}^{k} {\left(n - k\right)}^{n - k}}$
Assumptions:$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \{0, 1, \ldots, n\}$
TeX:
{n \choose k} \le \frac{{n}^{n}}{{k}^{k} {\left(n - k\right)}^{n - k}}

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \{0, 1, \ldots, n\}
Definitions:
Fungrim symbol Notation Short description
Binomial${n \choose k}$ Binomial coefficient
Pow${a}^{b}$ Power
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Range$\{a, a + 1, \ldots, b\}$ Integers between given endpoints
Source code for this entry:
Entry(ID("4e7120"),
Formula(LessEqual(Binomial(n, k), Div(Pow(n, n), Mul(Pow(k, k), Pow(Sub(n, k), Sub(n, k)))))),
Variables(n, k),
Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(k, Range(0, n)))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC