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📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 9! = 362880,\quad 4! = 24,\quad 3! = 6,\quad 2! = 2

📌 \frac{362880}{24 \cdot 6 \cdot 2} = \frac{362880}{288} = 1260

📌 Thus, the number of distinct sequencing orders is $ \boxed{1260} $.

📌 Question: If a fair six-sided die is rolled 4 times, what is the probability that exactly two rolls show a prime number and the sum of all four rolls is even?

📌 Solution: First, identify the prime numbers on a six-sided die: 2, 3, 5 → 3 primes; non-primes: 1, 4, 6 → 3 non-primes.

📌 Exactly two of the four rolls to be prime

📌 The sum of all four rolls to be even

📌 Step 1: Choose which 2 of the 4 rolls are prime:

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