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Home » Given $\cos \theta = \frac13$, compute: - Parker Core Knowledge

Given $\cos \theta = \frac13$, compute: - Parker Core Knowledge

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 To solve this problem, consider each position in the sequence of 5 digits. The first digit has 5 possible options: 0, 1, 2, 3, or 4. For each subsequent digit, it must differ from the one preceding it. Therefore, for each of the remaining 4 positions, there are 4 choices (since the digit cannot be the same as the one before it).

📌 Choices for the second digit: 4 (cannot be the same as the first)

📌 Choices for the third digit: 4 (cannot be the same as the second)

📌 Choices for the fourth digit: 4 (cannot be the same as the third)

📌 Choices for the fifth digit: 4 (cannot be the same as the fourth)

📌 Thus, the total number of sequences is:

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