use "total number of arrangements" - "forbidden options": those options where the three men DO sit together. Calculate each separately, then subtract.
Total number of arrangements = 7! ways to seat 7 people, regardless of limitations.
forbidden options: number of ways where the men DO sit together. Use a two step method for solving these "proximity" problems:
1) lump the men together into a single "entity" and figure out the number of ways of arranging the 4 women+single entity of "3 men": total of 5 "entities", or 5! different arrangements.
2) Think about the internal order of the men entity. There are 5!=120 different ways of placing arranging 4 women+entity, but the 3 men have 3! ways of arranging between them. For each of the 120 arrangements, you will get 3*2*1=6 arrangements depending on the internal arrangements of men within the entity. Thus, the final number of ways of arranging the 7 people with the men together is 5!*3!
Now, get back to our original calculation: "total number of arrangements" - "forbidden options = 7!-5!3! - or answer choice C.
