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Home » \[ y = 10 - 2x \] - High Altitude Science

\[ y = 10 - 2x \] - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Subcase 2b: Two odd non-primes → 1 × 1 = 1 choice

📌 Subcase 2c: Both even → 2 × 2 = 4 → contributes 0 odd

📌 Now, only subcases that yield even total odd count:

📌 Case 2a: odd non-primes count = 1 → total odd count = 1 (prime) + 1 = 2 → even → valid

📌 Case 2b: odd non-primes = 2 → total odd = 1 + 2 = 3 → odd → invalid

📌 Case 2a valid, others invalid

📌 So only 2a: 2 (prime assignments) × 2 (odd non-prime) × 2 (even non-prime) = 8

📌 Plus position arrangement: the even prime and odd prime are in different positions: $ \binom{4}{2} = 6 $ ways to assign which two slots get primes — but in this count, we are assigning to specific positions, so the $ \binom{4}{2} $ places the prime positions, then assign values.

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