Python glob multiple filetypes

Is there a better way to use glob.glob in python to get a list of multiple file types such as .txt, .mdown, and .markdown? Right now I have something like this:

projectFiles1 = glob.glob( os.path.join(projectDir, '*.txt') )
projectFiles2 = glob.glob( os.path.join(projectDir, '*.mdown') )
projectFiles3 = glob.glob( os.path.join(projectDir, '*.markdown') )

Maybe there is a better way, but how about:

import glob
types = ('*.pdf', '*.cpp') # the tuple of file types
files_grabbed = []
for files in types:
    files_grabbed.extend(glob.glob(files))

# files_grabbed is the list of pdf and cpp files

Perhaps there is another way, so wait in case someone else comes up with a better answer.