Distributing keys to A people, where
B people are required to unlock, requires:
A choose B-1 keys.

We can distribute following possible combinations:

Ex: 5 people, 2 required: 5 C 3 = 10

0123
012 4
01 34
0 234
 1234

We obtain A choose B-1, from seeing that we require
the combinations to be generated from A-B+1.

This is obtained from A-G+1 = B, 
People - GroupSize + 1 = Required,
G = A-B+1

A choose A-B+1 = A choose B-1