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on july 15 is chick fil a free - Parker Core Knowledge

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: A science journalist analyzes data where three integers are randomly selected from 1 to 50. What is the probability that the sum of the three numbers is divisible by 3?

📌 Question: How many distinct arrangements are there of the letters in the word POLLEN if the two Ls are indistinguishable and the two Es are indistinguishable?

📌 Question: A deck of $4n$ cards is shuffled, with $n$ cards labeled A, $n$ labeled B, $n$ labeled C, and $n$ labeled D. What is the probability that the first two cards drawn are of different labels?

📌 Question: Anne rolls a fair 10-sided die each hour. What is the probability that she rolls a prime number for the first time on the third roll?

📌 Since the crates are indistinguishable, we do not multiply by any symmetry factor (like $3!$), because we are already counting partitions into unlabeled sets.

📌 Question: An electrical engineer is designing a high-voltage transmission system with 7 relay stations, each of which can be set to one of two states: active (A) or standby (S). How many 7-state sequences exist such that no two adjacent stations are both active?

📌 We are to count the number of binary strings of length 7 (with letters A and S) where no two As are adjacent.

📌 Let $ a_n $ be the number of valid sequences of length $ n $ with no two consecutive As.

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