A hash table contains slots, and a hash function assigns values to these slots using a hash function. A collision is said to occur if more than one value hashes into any particular slot.

a$)$ Suppose a particular table contains $100$ slots, and $10$ values are inserted, calculate the probability of a collision.

b$)$ What is the maximum number of values that can be stored, in order to be at least $90\%$ sure that there will not be a collision?

Use the pbirthday and qbirthday functions in R to compute the final answers. Include the specific commands used for the computation.