Utensil that Absorbed Prohibited Food and Mixed with Other Utensils

Dear Rabbi! I work in a mixed workplace — religious and non-religious. They have allocated some kosher utensils separately for the religious, as well as a separate dishwasher, and the cleaner knows how to sort what is kosher and what is not and to place it accordingly. Yesterday someone was substituting for the cleaner and one of the secular workers found in the morning about five kosher glass cups in the non-kosher dishwasher (the cups are dairy, but in the dishwasher they wash utensils that have been used for both meat and dairy). She returned the cups to their usual place and they got mixed up with the rest of the utensils. (I will note that there are about 25 cups of this type in the office). What is the law regarding the cups? If they are prohibited for use — are all the cups now prohibited because there is no way to identify the cups that were in the non-kosher dishwasher today? Is there a way to kosher the cups? Thank you very much!

Dear …!
All the utensils are permitted for use. Since the prohibited utensils are nullified by the majority of the permitted utensils.

Shulchan Aruch, section Yoreh Deah, Ch. 102, paragraph 3.
Regarding utensils that can’t be scolded, all the authorities agree that this is the law.