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📰 Solution: Total combinations without restrictions: $\dbinom{9}{4} = 126$. Subtract combinations where both problematic startups are included: $\dbinom{7}{2} = 21$ (choosing 2 more from the remaining 7). Valid combinations: $126 - 21 = 105$. \boxed{105} 📰 Question: An epidemiologist models disease spread by assigning 6 unique patient IDs to 3 distinct risk categories, ensuring each category has at least one ID. How many assignments are possible? 📰 Solution: Use inclusion-exclusion. Total assignments: $3^6 = 729$. Subtract assignments missing at least one category: $3 \times 2^6 = 192$. Add back assignments missing two categories: $3 \times 1^6 = 3$. Valid assignments: $729 - 192 + 3 = 540$. \boxed{540}Question: An electrical engineer tests a new circuit with 5 identical resistors, each with a 10% probability of failing independently. What is the probability that exactly 2 resistors fail? 📰 Creditcard Review 9748541 📰 Edit Your Signature In Outlook Like A Proheres How To Make It Command Attention 326091 📰 Youll Fix Windows 10 Failures In Minutesheres The Ultimate Repair Tool 780093 📰 Mcdonalds Calories 4686586 📰 Inside The Oracle Certified Associate Test Youll Fail This And Why You Need To Pass It 8411392 📰 Download The Mobi Market Appits Changing How Millions Buy Daily 3148929 📰 Edia Exposed The One Trick That Unlocks Its Hidden Power 4720123 📰 Gm Part 3458409 📰 5Denial Not An Option Danica Collins Life Changing Journey Explained 8843395 📰 Name Extraction Rules Natural Language Processing 4551842 📰 Mcdonalds New Items 3401340 📰 Amazon And Yahoo Finally Shocked Us What Their Big Alliance Means For Your Daily Digital Life 4065345 📰 Trapped As A Noob Zombie After Brutal Prison Escape You Wont Believe What Happened Next 9844865 📰 Why Everyone Is Buying Meta Stockheres The Secret Buying Strategy You Need 2444924 📰 Milkweed Seeds Youre Scatterin Across Your Yardyou Wont Believe What Happens Next 2597040