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# GATE | GATE-CS-2014-(Set-3) | Question 65

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?

(A)

(97 × 97 × 97)/1003

(B)

(99 × 98 × 97)/1003

(C)

(97 × 96 × 95)/1003

(D)

(97 × 96 × 95)/(3! × 1003)

Explanation:

Simple Uniform hashing function is a hypothetical hashing function that evenly distributes items into the slots of a hash table. Moreover, each item to be hashed has an equal probability of being placed into a slot, regardless of the other elements already placed.

```Probability that the first 3 slots are unfilled after the first 3 insertions =
(probability that first item doesn\'t go in any of the first 3 slots)*
(probability that second item doesn\'t go in any of the first 3 slots)*
(probability that third item doesn\'t go in any of the first 3 slots)

= (97/100) * (97/100) * (97/100) ```

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