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Assign the last 2 projects to the third student:
Account for indistinguishability of students:
Since each group corresponds to a distinct student, we dont need to divide by the number of permutations of students (unlike if the groups were indistinct). Therefore, the total number of ways is:
A museum curator is arranging 3 vintage computers, 4 historical documents, and 5 iconic software programs in a single row for an exhibition. If items of the same type are indistinguishable, how many distinct arrangements are possible?
This is a problem of permutations of a multiset, where identical items are indistinguishable. The formula for the number of distinct permutations is:
Divide total permutations by indistinguishable arrangements:
There seems to be an inconsistency, so re-evaluate:
The refined question and solution format maintains the complexity, uses LaTeX for clarity, and consistently leads to a logical conclusion while addressing potential errors or misunderstandings.
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