
die Einrichtung
furnishings
The collection of furniture, rugs, lamps, and other objects in a room or apartment.
Die neue Wohnung hat eine sehr helle und moderne Einrichtung.
The new apartment has very bright and modern furnishings.
furnishings / institution / setup
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furnishings
The collection of furniture, rugs, lamps, and other objects in a room or apartment.
Die neue Wohnung hat eine sehr helle und moderne Einrichtung.
The new apartment has very bright and modern furnishings.

institution
An institution or organization that serves a particular public, social, or economic purpose, such as a hospital, school, or government office.
Der Kindergarten ist eine wichtige soziale Einrichtung für Familien.
The kindergarten is an important social institution for families.

setup
The process of setting up, installing, or organizing something, for example software or a new system.
Die Einrichtung des neuen Netzwerks hat den ganzen Vormittag gedauert.
Setting up the new network took the entire morning.
'Die Einrichtung' (furnishings/institution/setup) is the noun related to the separable verb 'einrichten' (to furnish/set up). The verb means to put furniture in a room or to install something technically. The noun describes the result or the process of this action.
Wir müssen das neue Büro noch komplett einrichten.
We still have to furnish the new office completely.
You can recognize the meaning from the context: if it is about furniture and style, it refers to the furnishings of an apartment. If it is about organizations like schools or offices, it means an institution. If it is about technology or accounts, it means the setup or installation process.
Ihre Einrichtung ist sehr geschmackvoll.
Her furnishings are very tasteful.
When it is about furniture and decoration, 'Einrichtung' is often combined with adjectives that describe a style, e.g. 'moderne' (modern), 'klassische' (classic), 'gemütliche' (cozy), or 'komplette' (complete) furnishings.
Sie wünscht sich eine helle und moderne Einrichtung für ihr Wohnzimmer.
She wants bright and modern furnishings for her living room.
As an institution, 'Einrichtung' is often further specified with adjectives such as 'öffentlich' (public), 'sozial' (social), 'staatlich' (state-run), or 'medizinisch' (medical).
Das Krankenhaus ist eine wichtige medizinische Einrichtung in der Stadt.
The hospital is an important medical institution in the city.
In the meaning 'Setup/Installation', a genitive or 'von' + dative is often used to specify what is being set up. For example: 'die Einrichtung des Kontos' (the setup of the account) or 'die Einrichtung von dem neuen Programm' (the setup of the new program).
Die Einrichtung des neuen WLAN-Routers dauerte nur wenige Minuten.
Setting up the new Wi-Fi router took only a few minutes.
organization
Organisation and Einrichtung can both refer to an institution that carries out work. Organisation tends to emphasize the group, its members, and their joint activities, while Einrichtung emphasizes the specific public or social purpose. Organisation works for the group taking action; Einrichtung works for the place or service with this purpose.

Die Einrichtung bietet Familien mit wenig Geld kostenlose Beratung.
The institution offers free advice to families with little money.
Die Organisation unterstützt Familien mit wenig Geld.
The organization supports families with little money.