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A group of 11 scientists are working on a secret project, the materials of which are kept in a safe. They want to be able to open the safe only when a majority of the group is present. Subsequently the safe is provided with a number of different locks, and each scientist is given the keys to a certain number of these locks. How many of these locks are required, and how many keys must each scientist have?
I guess number of locks required should be 11C5 + 1. Can someone please verify this and also I can't figure out how to calculate number of keys