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how much is a stamp today - Belip

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 So the number of distinct permutations is:

📌 Question: A primatologist records vocalizations from 6 distinct orangutans, assigning each a unique identification code of the form ABCDEF, but permutes only three specific digits—A, B, and C—while the rest remain fixed. In how many ways can the system generate a valid code if A must come before B?

📌 Solution: The code fixes 4 digits (D, E, F) and permutes only A, B, C in the remaining 3 positions. The total number of permutations of A, B, C is $3! = 6$. Among these, the number of permutations where A comes before B is exactly half, since in half the arrangements A precedes B and in half B precedes A (the cases are symmetric).

📌 Thus, number of valid codes where A comes before B is:

📌 Since the outer digits are fixed, this counts the number of valid codes satisfying the constraint.

📌 Combine the results from steps 1 and 2:

📌 Next, find $ xy $. Use the identity:

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