For 8 species, the number of permutations is calculated as:

February 22, 2026

For 8 species, the number of permutations is calculated as:

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\text{Area} = \frac{1}{2} \times \text{diagonal}_1 \times \text{diagonal}_2 = \frac{1}{2} \times 8 \times 8 = \boxed{32}
---**Question:** An ornithologist is studying a flock of 8 distinct bird species migrating together. In how many ways can the ornithologist label these species with unique tags numbered 1 through 8?
To solve this problem, we need to determine the number of permutations of 8 distinct bird species, as each species is assigned a unique tag. The number of permutations of \( n \) distinct objects is given by \( n! \) (n factorial).
8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1
Calculating this step-by-step:
\times 7 = 56

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