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51 people (a1,a2,......,a51) meet and shake hands in a circular fashion. In other words, there are totally 51 handshakes involving the pairs (a1, a2),(a2,a3),......,(a50,a51),(a51,a1). Then the size of the smallest set of people such that the rest have shaken hands with at least one person in the set is

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A toy train produces 10 different tunes when it moves around a circular track of radius 5 meters, at 10 meters per minute.However the toy train is defective and it now produces only two different tunes at random. What is the probability that the toy train produces 6 consecutive music of the same type (1 in ----)? 64, 6, 36, 32 An old lady has certain gloves and hats in her basket. She has around 35 gloves and 42 hats in her collection. She went to his Grandchildren on a certain occasion. She decided to gift her grandchildren few hats. She had 3 grandchild. So how many attempts she will have to make to ensure that smallest will get 1, and second will get 2, and eldest will get 3 hats.