There is a cabinet consisting of m members. Cabinet materials are stored in safe. How many lock should the safe have, and how many keys should be made for these locks, and how these keys have to be distributed among the cabinet members such that the safe can be open if and only if at least j members of the cabinet are present?
Attempt: Should I approach this by Stirling numbers of second kind. Where first I have to find the number of locks, then distribute in S(n,k) ways where n is the number of locks and k is the number of keys. Still I am unable to justify?