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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?

1. (97 × 97 × 97)/100³
2. (99 × 98 × 97)/100³
3. (97 × 96 × 95)/100³
4. (97 × 96 × 95)/(3! × 100³)

Correct answer: (97 × 97 × 97)/100³

Solution

The correct option calculates the probability that each of the first three slots remains unfilled after three insertions, assuming uniform hashing. Since there are 100 slots and 97 of them are available for each insertion, the probability for each of the three slots to remain unfilled is (97/100), leading to (97 × 97 × 97)/100³.

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