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📅 May 12, 2026 👤 scraface

May 12, 2026

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📌 We compute the number of favorable outcomes where the two marbles are of different colors.

📌 = (15 - 2) + (15 - 4) + (15 - 6) + (15 - 8) + (15 - 10) + (15 - 12) + (15 - 14)

📌 Each such triple corresponds to one favorable outcome, and all triples are unordered but distinct — since we are choosing sets, each AP is counted once as a set.

📌 Three fair 6-sided dice are rolled. What is the probability that exactly two dice show the same number, and the third shows a different number?

📌 We want exactly one pair and one different number.

📌 Step 1: Choose the number that appears twice: 6 choices.

📌 Step 2: Choose the different number: 5 choices (different from the first).

📌 How many distinct arrangements of the letters in the word MATHEMATICS are there such that the two Ms are not adjacent?

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