Naive Bayes Multinomial, independence assumption misunderstood
Their outcomes X are dependent because they must be summed to n  


If you are really want to model multiple experiments probabilistically, please do not forget the normalization constant that make the unnormalized quantity normalized by integrating/summing them to one.   

Multinomial Naive Bayes model, as described by Manning et al (2008), estimates the conditional probability of a particular word/term/token given a class as the relative frequency of term t in documents belonging to class c:  



Thus this variation takes into account the number of occurrences of term t in training documents from class c, including multiple occurrences Not multiple experiments.  

see The Naive Bayes Text Classifier