обоје / оба / обе

To express 'both' accurately in Serbian, follow these rules according to noun gender, grouping, and meaning:

1. Forms by Gender: оба and обе
• оба is used with pairs of masculine nouns or pairs of neuter nouns in their paucal form (e.g., оба професора - both professors; оба писма - both letters; оба села - both villages). Note: If a pair consists of mixed genders—most notably a mixed male-and-female pair (such as син и ћерка or брат и сестра)—you cannot use оба; you must use the collective form обоје.
• обе (in Ekavian) or обје (in Ijekavian) is used exclusively with feminine nouns, taking the feminine paucal form, which formally coincides with the nominative/accusative plural ending (e.g., обе књиге - both books; обе сестре - both sisters; обе ствари - both things).
• Declension in Oblique Cases: Both words decline across oblique cases: for masculine/neuter оба, the genitive is обају and dative/locative/instrumental is обама (e.g., са обама пријатељима); for feminine обе, the genitive is обеју (or Ijekavian обију) and dative/locative/instrumental is обема (or Ijekavian објема) (e.g., у обема књигама). In everyday speech, prepositional constructions with invariable оба / обе often appear, but oblique forms are standard in careful writing.

2. Mixed Pairs, Offspring, Alternatives, and Pluralia Tantum: обоје
• обоје is primarily a collective numeral (collective numerals). It is standardly used for mixed male-and-female human pairs (e.g., Марко и Милица, син и ћерка), pairs of young beings and offspring (e.g., обоје јагњади, обоје деце), and combinations of nouns belonging to different genders. While phrases like обоје родитеља occur when emphasizing the two distinct individuals (father and mother), masculine count nouns like родитељи and супружници standardly and frequently take оба (оба родитеља, оба супружника).
• обоје functions as an independent neuter quantifier meaning 'both / one and the other' (и једно и друго) when referring to two alternatives or actions: Хоћеш чај или кафу? — Обоје! (Do you want tea or coffee? — Both!).
• Numeral Adjectives with Pluralia Tantum and Sets: With plural-only nouns (pluralia tantum) or nouns denoting sets, pairs, and collective groups, the declinable numeral adjectives обоји (masculine plural), обоје (feminine plural), and обоја (neuter plural) are used instead of оба / обе: обоја врата (both doors; neuter pl.), обоје маказе (both scissors; feminine pl.), обоје чарапе (both pairs of socks; feminine pl.), or обоји сватови (both wedding parties; masculine pl. collective).

3. Two Male Persons: оба vs. обојица
When referring specifically to two male persons, you can use оба or the numeral noun обојица:
• Оба acts as a determiner taking paucal forms: оба дечака, оба професора.
• Обојица is a numeral noun ending in -ица that stands alone or governs a genitive plural: обојица студената, обојица дечака. In past compound tenses, masculine plural semantic agreement is standard modern usage (Обојица су дошли), alongside formal agreement ending in -а with a plural auxiliary (Обојица су дошла).

4. Verb Agreement
• With оба and masculine nouns, the past participle canonically takes paucal agreement ending in -а (Оба брата су радила), though masculine plural agreement ending in -и is also common in speech (Оба брата су радили).
• With обе and feminine nouns, the verb takes feminine plural agreement: Обе сестре су радиле.
• With обоје referring to people, masculine plural semantic agreement (Обоје су били овде) and formal neuter singular agreement (Обоје је било овде) are both standard. Neuter singular agreement is standard when selecting between two alternatives or with neuter collective nouns: Обоје је било тачно; Обоје деце је заспало.