Suppose I have a set of characters, say $\{a-z,A-Z,0-9\}$ $(n=62)$. Then I select a random permutation each containing $10$, e.g. $k=10$, characters. What would be the probability of a collision — a previously selected permutation gets selected again?
2026-03-28 07:51:36.1774684296
Probability of a Collision in Selection of Permutations
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The distinction discussed in the Comments is whether symbols can be repeated or not in the string of 10. For example, is "AAbe2de313" permitted, or does it have to be something like "13daCVse82"?
The first way there are $62^{10}$ possibilities, and the second way there are $P(62,10) = 62!/(62-10)!\,.\,$ (In the usual terminology 'combinations' are not involved in either of these.)
In each case, the probability of repeating exactly the same characters in exactly the same order in any one try is the reciprocal of the number of possibilities.
Your statement is a little vague. If your question is not answered here, please leave a comment.