fan / range
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fan
An object, usually made of paper or fabric, that can be folded up and used to create a current of air by moving it back and forth in the hand.
Bei der Hitze im Theatersaal war sie froh über ihren Fächer.
In the heat of the theater hall, she was glad to have her fan.
The word 'Fächer' (fan/range) is related to 'Fach' (compartment, field). A hand fan visually consists of many folded 'Fächer' (sections). This idea of division also carries over to the abstract meaning of a spectrum of topics.
Der Schrank hat ein unteres Fach für Schuhe.
The cabinet has a lower compartment for shoes.
You can recognize the meaning from the context. If it refers to an object used to fan air toward oneself, it means a hand fan. If it is about a selection of topics or possibilities, often with adjectives like 'breit' (broad) or 'groß' (large), it means a spectrum or range.
Sie klappte ihren Fächer auf und wedelte sich Kühlung zu.
She opened her fan and fanned herself to cool down.
In the abstract meaning, 'Fächer' (range/spectrum) is often used with the preposition 'an' and the dative plural. The structure is: 'ein Fächer an [noun in the dative plural]' (a range of [plural noun]).
Die Firma bietet einen ganzen Fächer an Dienstleistungen an.
The company offers a whole range of services.
selection / choice
'die Auswahl' and 'der Fächer' can both describe a variety of possibilities. 'die Auswahl' is the normal word when you can choose from several things, for example in a shop or on a list. 'der Fächer' more often means a broad range or spectrum of related topics, offers, or possibilities. This word sounds a little more elevated and is not used for every everyday situation. They can be confused in phrases like 'breite Auswahl' (wide selection) and 'breiter Fächer' (broad range). In everyday language, 'Auswahl' is often more natural; 'Fächer' fits better when you want to emphasize the full breadth of an area.
Die Beratungsstelle bietet einen breiten Fächer an Hilfen für Familien.
The counseling center offers a broad range of support for families.
Für die Prüfung hat er eine Auswahl wichtiger Texte bekommen.
For the exam, he was given a selection of important texts.