Learn Italian: Non c'è nessuna possibilità di cambiare la situazione. - There is no possibility of changing the situation.

Nessuna describes the noun possibilità, which is feminine. Because possibilità starts with a consonant (the letter 'p'), we use the full feminine form nessuna. You would only use nessun' (with an apostrophe) if the feminine noun started with a vowel, and nessun (no apostrophe) is for masculine nouns.

Why are both non and nessuna used here? Isn't that a double negative?

Yes, and double negatives are often required in Italian! When a negative word like nessuna comes after the verb (here, c'è), you must also put non before the verb. English says 'There is no possibility', but Italian literally says 'There is not no possibility'.

How do we know possibilità is feminine so we can match nessuna to it?

Almost all Italian nouns ending in an accented -tà (like possibilità, città, università) are feminine. As a bonus rule to remember, these nouns are invariable, meaning their endings never change in the plural.

Why do we use the preposition di before cambiare?