In the book: "Mathematical Statistics and Data Analysis" by John Rice, Example K in chapter 1, Rice writes:
What does dividing the letters into subgroups do in this case? Isn't this question just asking how many ways you can rearrange the nine letters? What's the intuition behind dividing them into groups?
Isn't this question just asking how many ways you can rearrange the nine letters? Yes
What's the intuition behind dividing them into groups? Since the order within the group doesn't matter, diving into groups let you pick, where to put the 2's, the 3's and the 4's, and in how many forms, which is the goal in this case.