Question regarding logistic regression

Is it possible to use logistic regression when the predictor variables are dichotomous, but that the data was gathered from checkboxes- meaning the students who answered the questions were able to select more than one choice- They then predict a dichotomous variable? If not, is there a way around this or another analysis?
For example-
From which of the following did you hear about the program
Mark all that apply

These would then be used to predict those who particatpe or did not participate in the program.:shakehead