P&C isro

Eleven scientists are working on a secret research project of ISRO. They wish to lock up all the documents regarding the project in a cabinet such that the cabinet can be opened if and only if atleast six of these scientists are present, and for that certain number of locks and keys are used Satisfying the conditions mentioned above.

1. The smallest number of locks needed is
(a) 252 (b) 250 (c) 460 (d) 462

2. The smallest number of the keys to the locks each scientist must carry is
(a) 252 (b) 250 (c) 460 (d) 462