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Thus, the number of distinct ways to allocate the sunlight is:
Total number of letters: $ 3 + 2 + 3 = 8 $
The number of distinct permutations (anagrams) of a multiset is given by:
Thus, the number of distinct anagrams is:
This is a problem of counting the number of multisets of size 5 (prototypes), where each element is chosen from a set of 3 options (A, B, C), and the order doesnt matter (prototypes are indistinguishable).
This is equivalent to counting the number of integer solutions to:
Thus, the number of distinct combinations of dopant assignments is:
Each of the 7 distinct phonemes has 3 choices for its evolutionary path (old, intermediate, new). Since the phonemes are distinguishable and the evolution is independent, the total number of possible outcomes is:
Thus, the total number of evolutionary outcomes is:
We are to distribute 6 identical solar trackers (indistinguishable) into 4 distinguishable sites (labels), with the constraint that no site receives more than 2 trackers.
