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📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 To solve this problem, we need to calculate the total number of permutations of the fruits Alice will eat, considering that fruits of the same type are indistinguishable.

📌 Calculating each factorial, we have:

📌 A cooking club consists of 5 members and 3 guests. In how many distinct ways can they be seated around a circular table, assuming all individuals are distinguishable?

📌 How many distinct 7-letter words can be formed using the letters in BALLOON if each letter can be used only as many times as it appears in the word?

📌 The word BALLOON consists of the following letters: B (1), A (1), L (2), O (2), N (1). We need to count the number of distinct permutations of these letters.

📌 The formula for permutations of multiset is:

📌 Thus, the number of distinct 7-letter words is:

📌 First, consider the residue classes modulo 3 for numbers from 1 to 50. Numbers can have residues 0, 1, or 2:

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