Simple Uniform Hashing and Load Factor

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The number of keys stored in the hash table divided by the capacity is called load factor. Simple Uniform Hashing , any given element is equally likely to hash into any of the slots in the hash table.
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Hi is it possible to know what the maximum number of elements would be in a slot rather than the average. Using your example, if we have 1000 keys would the maximum/worst case number of elements in a slot be 1000?

yunglex