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kilroys breadsticks of the month - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 P(9, 6) = \frac{9!}{(9 - 6)!} = \frac{9!}{3!}

📌 9! = 362880,\quad 3! = 6

📌 \frac{362880}{6} = 60480

📌 Thus, the total number of unique check-in codes is $\boxed{60480}$.

📌 Question: An industrial hygienist in Los Angeles is analyzing exposure levels in 6 different work zones, each with 3 safety zones. If 2 zones are randomly selected for an immediate inspection, what is the probability that both are in the same work area (i.e., same high-risk level), assuming each work area contains exactly 2 zones?

📌 Solution: There are 6 work areas, each with 2 zones, making a total of $6 \times 2 = 12$ zones. Since 2 zones are selected at random, the total number of ways to choose 2 zones is:

📌 \binom{12}{2} = \frac{12 \times 11}{2} = 66

📌 To find favorable outcomes (both zones in the same work area), note that each work area has $\binom{2}{2} = 1$ way to choose both zones. With 6 work areas, the number of favorable outcomes is:

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