Gate Exam Programming

Consider a hash table with 100 slots. Collisions are resolved using chaining. Assuming
simple uniform hashing, what is the probability that the first 3 slots are unfilled after the first
3 insertions?

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Gate Other Question
if a2 + b2 + c2 = 1, then ab + bc + ac lies in the interval.... a gambler has 4 coins in her pocket. two are double headed one is doubled tailed and one is normal.the coins can not be distinguished unless one looks at them.
the gambler takes a coin at random,opens her eyes and sees the the upped face of the coin is a head .what is the probability that the lower face is a head?