кілька/багато/мало + Genitive Plural

These words are known as indefinite-quantitative numerals (неозначено-кількісні числівники). Note that багато, кілька, and декілька decline similarly to the numbers два, три, чотири. For the Instrumental case, багато has two parallel valid forms: багатьма and багатьома. Similarly, кілька becomes кількома, and декілька becomes декількома.

1. Case Government (Direct Cases)
When the quantifier is the subject (Nominative) or the direct object (Accusative for inanimate nouns), it 'governs' the noun:

• Countable: багато / кілька + Genitive Plural (e.g., багато столів - many tables).
• Uncountable: багато / мало + Genitive Singular (e.g., мало часу - little time).

2. Case Agreement (Oblique Cases and Animate Accusative)
In other cases (Dative, Instrumental, Locative) and for the Accusative of animate nouns (people and animals), the quantifier must agree with the noun in the plural case. In the Accusative case, the quantifier takes the Nominative form for inanimate objects (бачу кілька столів) and the Genitive form for animate objects (бачу кількох друзів).

• Declinable (багато, кілька, декілька): These agree with the noun. For example: з багатьма/багатьома друзями (with many friends - Instrumental), у кількох містах (in several cities - Locative), бачу багатьох друзів (I see many friends - Accusative Animate). Декілька declines just like кілька: декількох (Gen./Loc./Acc. animate), декільком (Dat.), декількома (Inst.).
• Restriction on 'мало': The quantifier 'мало' (and 'чимало') is generally not used in oblique cases. To express 'with few' or 'to few', use the declinable word небагато. For example: з небагатьма свідками (with few witnesses).

3. Verb Agreement
When a phrase with багато or кілька is the subject, the verb can take either the plural or the singular (neuter in the past tense). Plural is often preferred for animate subjects (people) or active actions, while singular/neuter is common for inanimate objects or passive existence. For example: Багато студентів склали іспит (plural) or Багато студентів склало іспит (neuter singular).

4. Кілька vs. Декілька
These are synonyms meaning 'a few' or 'several'. While often interchangeable, кілька is more productive in word formation (e.g., кільканадцять - 'some dozen', кількаденний - 'lasting several days') and is often preferred in modern speech for its brevity. Декілька is also common but lacks this extensive word-building capacity.