Question

If h is any hashing function and is used to hash n keys in to a table of size m, where n<=m, the expected number of collisions involving a particular key x is:

(A) Less than 1
(B) Less than n
(C) Less than m
(D) Less than n/2

What I figured out is, it should be less than n but I’m not sure.

Answer 1

You best read up on the Birthday paradox.

Here are some links:

Birthday problem

understanding-the-birthday-paradox

And a quote from the second link:

Here are a few lessons from the birthday paradox:

• sqrt(n) is roughly the number you need to have a 50% chance of a match with n items. sqrt(365) is about 20. This comes into play in
  cryptography for the birthday attack.
• Even though there are 2^128 (1e38) GUIDs, we only have 2^64 (1e19) to use up before a 50% chance of collision. And 50% is really, really
  high.
• You only need 13 people picking letters of the alphabet to have 95% chance of a match. Try it above (people = 13, items = 26).
• Exponential growth rapidly decreases the chance of picking unique items (aka it increases the chanes of a match). Remember: exponents
  are non-intuitive and humans are selfish!