I am a beginner, so I'm not 100% on this, but I think dei is di+i and degli is di+gli. Gli is the plural of lo, the masculine article used before s+consonant, ps, gn, and z (and there may be other cases that I'm not aware of). So you'd say dei paesi and degli studenti. Native speakers, feel free to correct if I'm off here!

@Giada grazie mille!

You can use the same rule of the definite articles I and GLI. - Dei= Di + i. You can use it for masculine plural nouns which start with a consonant. e.g.: dei libri, dei tavoli, dei bicchieri, dei pantaloni. - Degli= di+ gli. You can use it for masculine plural nouns which start with a vowel, s + consonant, z, y, ps, pn, x or gn. e.g.: degli amici, degli studenti, degli zaini, degli yogurt, degli psicologi.