"He is the baby of the family."
Translation:C'est le bébé de la famille.
This is a rule you will have to apply VERY often on Duolingo. In French, "c'est" (sing.) and "ce sont" (plural) are used in a large variety of expressions, when a pronoun (it, she, he, they) is subject of verb "être" and followed by a nominal group, ie: article (+ adjective) + noun. - it is + noun => c'est - she is + noun => c'est - he is + noun => c'est - they are + noun => ce sont
A rule is a rule... but, luckily all rules have their exceptions.
when "il est" (or elle est or ils/elles sont) is followed by "the" + a noun expressing a "single status", you can use "il est" or "c'est" interchangeably:
he is the president of the republic (only one person has that status) = c'est le président de la république or il est le président de la république.
she is my only cousin = c'est ma seule cousine or elle est ma seule cousine.
she is Peter's second wife = c'est la seconde femme de Peter or elle est la seconde femme de Peter.
So, by exception, Duo should accept "il est LE bébé de la famille" (there is only one)
As you can read on the 4th post on this page, "il est le + noun" can be an exception to the rule that "il est + modified noun" has to be changed to "c'est + modified noun".
So, it is possible that Duolingo has not offered that exception as a valid answer for all sentences containing "he/she is the + noun".
Here is a good resource to understand when to use "il est" and "c'est": http://french.about.com/library/weekly/aa032500.htm
To get past the duolingo "dink dunk" of a wrong response, just remember the form: "c'est" if the noun has "the" or "my" in front of it (or almost any other modifier). "Il/Elle est" otherwise.
Don't overthink this and get caught up in the linguistic jargon. Learning French is not hard. Four year old French kids do it every day.
When "des" is a contraction of "de+les", it is:
- either a possessive case (le bébé des parents)
- or the indirect object of a verb constructed with preposition "de" (il parle des enfants = he talks about the children).
But "des" is also the plural indefinite article (that does not exist in English), and in this case, it is not a contraction of de+les:
- je prends un verre (singular) = I take a glass
- je prends des verres (plural) = I take (some) glasses
When it comes to "de", it is only a preposition, with a wide array of usages, including tricky ones:
Expressions of quantity:
- j'ai beaucoup de verres - not "de + des verres": in this case, the article "des" disappears to give precedence to "de", which belongs to "beaucoup de" (prepositional phrase), for euphony reasons.
- je n'ai pas de verres - not "de + des verres", again for euphony reasons.