so I have a quiz with 10 questions.
Each question comes from a category with a specific number of questions (36, 21, 23, 17, 32, 19, 27, 15, 16, 13)
If each category is only used once in each quiz, how many different quizzes are possible?
I have looked, but the "stars and bars" solution is incorrect and so I am now not sure and my stats was a LONG time ago.!
So wanted to try the permutations ie n! / (n - m)! but excel on my mac will not exceed 170! ...
It's simply Rule of Product and the answer should be $$36\cdot 21\cdot 23\cdot 17\cdot 32\cdot 19\cdot 27\cdot 15\cdot 16\cdot 13 = 15139812280320$$ Stars and bars is not used here because we don't have identical questions in each category. Stars and bars is used when we have identical objects and we group them.