combinatorics – Reverse gap method in permutations and combinations

This is my second attempt at posting this question as last time I wasn’t able to explain myself properly. But I have put it together in a completely different way this time.

There are 10 distinct people sitting in a row in a fixed order and 4 people are to be selected such that no two of them are consecutive. The way our sir solved this question is- the number of people left after selecting 4 would be (10-4)= 6. Now taking six people, there are 7 gaps around them. The 4 people that were selected could have come from any 4 of the 7 gaps around these 6 people (as these 4 were non-consecutive). And the number of ways of selecting 4 gaps out of 7 is 7C4. So the final answer is 7C4. This is called ‘reverse gap method’ by our sir.

Though it seems correct I can’t quite feel comfortable with this logic. Can someone make this method clear?