Permutation and Combination problem

Professor Franklin can have all five of his graduate students – Albert, Billy, Carlie, Dennis, and Emily – accompany him to the research conference. Alternatively, he can decide to take only four, three, two, or one of the students. How many of the possible groups of graduate students attending the conference include Carlie?


What am I doing wrong here?

The correct answer is 16

"Professor Franklin can have all five of his graduate students" – Albert, Billy, Carlie, Dennis, and Emily – accompany him to the research conference

That makes total cases 15+1 = 16
You forgot to include 1st line of the question.

Ohhh okay thanks Aditya!!

can you elaborate it please.
i thought it has to be 5c4+5c3…