What is the probability that in a box of a dozen donuts picked from 14 flavors there’s no more than 3 flavors in the box?

Problem

Dave’s Donuts offers 14 flavors of donuts (consider the supply of each flavor as being unlimited). The “grab bag” box consists of flavors randomly selected to be in the box, each flavor equally likely for each one of the dozen donuts. What is the probability that at most three flavors are in the grab bag box of a dozen?

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On Programming Languages; Why My Dad Went From Programming to Driving a Bus

In Data Science from Scratch, a book introducing data science using Python, Joel Grus said the following about R (pg. 302):

Although you can totally get away with not learning R, a lot of data scientists and data science projects use it, so it’s worth getting familiar with it.

In part, this is so that you can understand people’s R-based blog posts and examples and code; in part, this is to help you better appreciate the (comparatively) clean elegance of Python; and in part, this is to help you be a more informed participant in the never-ending “R versus Python” flamewars.

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