### Instruction: I have 7 books I want to arrange on a shelf. Two of them are math books, and one is a physics book. How many ways are there for me to arrange the books if I want to put the math books next to each other, and put both of them to the left of the physics book? (Note that all the books are distinguishable.).### Response: This problem involves counting the number of possible arrangements, which is a type of permutation.
Since the math books have to be next to each other, I can think of them as a single unit, and then I have 6 units to arrange: MM, P, and the other 4 books.
However, within the MM unit, the two math books can be swapped, so there are 2 ways to arrange them.
So, the total number of ways to arrange 6 units, where one of them has 2 ways to arrange itself, is 6! * 2.
But this is not the final answer, because I also have to consider the constraint that the MM unit has to be to the left of the P unit.
This means that half of the arrangements I counted are invalid, because they have P to the left of MM.
So, I have to divide the previous result by 2, to get the number of valid arrangements.
Therefore, the final answer is (6! * 2) / 2, which simplifies to 6!.