Solution: We are given a multiset of 12 soil cores: 3 from Plot A, 2 from Plot B, and 1 each from Plots C, D, E, and F. The total number of distinct sequences (arrangements) in which these indistinct items can be arranged is a multinomial coefficient:

Wed, 06 May 2026 08:32:03 +0000

**Soil Diversity Meets Data Science: The Hidden Complexity Behind Agricultural Multisets**
*Why understanding soil arrangement patterns is gaining quiet traction across U.S. research and farming communities* --- ### A Surprising Pattern in Soil Composition We are given a multiset of 12 soil cores: 3 from Plot A, 2 from Plot B, and one each from Plots C, D, E, and F. That’s 12 distinct samples in a single, structured dataset—each core identical within its plot but distinct across plots. What makes this simple setup worth studying? Each arrangement reveals hidden order beneath seemingly natural randomness. The number of unique ways these indistinct soil cores can be sequence-aligned across plots isn’t guesswork—it’s a precise math concept: the multinomial coefficient.