Ways to nest some of seven distinct dolls

Kaushik owns $7$ nesting dolls, all of different sizes. A nesting uses two or more of the dolls, each placed inside the next larger one chosen, so sizes shrink from outside to inside. How many different nestings can he make?

$120$. Any set of at least two dolls nests in exactly one way (largest outside, and so on inward). So count subsets of size $\ge2$: $2^7-1-7=120$.