14. Each post published on the Instagram page of the Math Olympiad must have 2 or 3 hashtags, chosen from 10 predefined hashtags. The administrators of the page follow this rule: if the hashtag "\#ItaMO" is present in a post, "\#cese2020" must also be present (these are two of the 10 hashtags). In how many ways can the set of hashtags to be inserted in a post be chosen?
(A) 120
(B) 93
(C) 165
(D) 90
(E) 129
(14) The correct answer is $(E)$.

The possible choices of 2 hashtags are a total of $1+\frac{9 \cdot 8}{2}=37$ (respectively: the pairs of hashtags where \#ItaMO appears and those where it does not).

The possible choices of 3 hashtags are a total of $8+\frac{9 \cdot 8 \cdot 7}{3 \cdot 2}=92$ (respectively: the triples of hashtags where \#ItaMO appears and those where it does not).

In total, the set of hashtags can be chosen in $37+92=129$ ways.

Question proposed by Riccardo Zanotto.