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what happens if you match one number on powerball - Network4

📅 May 20, 2026 👤 scraface

May 20, 2026

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📌 Question: A science educator designs a digital learning module where students complete 7 sequential interactive tasks, each tagged with one of three difficulty levels: Easy (E), Medium (M), and Hard (H). If each task is assigned a difficulty uniformly at random, what is the probability that exactly two tasks are Hard and no two Hard tasks are consecutive?

📌 Solution: We are to compute the probability that, in a random assignment of difficulty levels (E, M, H) to 7 tasks, exactly 2 are Hard and no two Hard tasks are adjacent.

📌 Now, count number of sequences with exactly 2 Hs and no two Hs adjacent.

📌 Step 1: Choose positions for the 2 Hard tasks such that they are not adjacent.

📌 We need to choose 2 positions from 7 such that they are not consecutive.

📌 The number of ways to choose 2 non-consecutive positions from 7 is:

📌 Alternatively: place 2 non-adjacent Hs. Imagine placing 5 non-H tasks (each E or M), creating 6 possible gaps (before, between, after) to insert Hs. We choose 2 distinct gaps:

📌 For each such placement, the remaining 5 positions must be assigned either E or M — 2 choices each.

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