Permutations and combinations

A wise old woman calls upon all her 7 sons at her eleventh hour and hands them over the keys of a box in which she keeps all her precious jewellery. She tells them that she has locked the box with multiple locks so that the box can be opened only when the majority of them are present with the keys that she gives them. After giving each of her sons the keys of certain locks she takes her last breath. How many locks does she use to secure her jewellery and how many keys does she hand over to each of the seven sons?

HERE, when calculating number of locks why are we just considering group size 3 and not 2 and 1 as well.