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📰 Solution: Since one marker is mandatory, choose 1 additional marker from the remaining 3: $\dbinom{3}{1}$. Then, select 2 sequences from 6: $\dbinom{6}{2}$. Multiply these: $\dbinom{6}{2} \times \dbinom{3}{1} = 15 \times 3 = 45$. The total number of valid combinations is $\boxed{45}$.Question: A tech startup founder has 8 potential investment opportunities and wants to diversify by selecting 5, but two specific opportunities are mutually exclusive. How many valid investment portfolios can be formed? 📰 Solution: First, calculate the total number of ways to choose 5 opportunities from 8 without restrictions: $\binom{8}{5} = 56$. Next, subtract the number of invalid portfolios that include both mutually exclusive opportunities. If both are selected, the remaining 3 are chosen from the other 6: $\binom{6}{3} = 20$. Thus, the valid portfolios are $56 - 20 = 36$. The final answer is $\boxed{36}$. 📰 Question: A science educator designs a 6-module interactive curriculum using 3 physics simulations, 2 chemistry experiments, and 1 biology lab. How many distinct arrangements are possible if the biology lab must not be placed after the chemistry experiments? 📰 Lightpath Stock 📰 Chase Vs Bank Of America 📰 Dash Roblox 📰 Wells Fargo Change Card Design 📰 Icon Changer For Windows 📰 Cellular Phone Plan Comparison 803289 📰 Tom Clancys Ghost Recon Future Soldier 📰 Animereborn 5402077 📰 Unlock Your Carfax Historybut First Prove Youre Authorized 8695668 📰 Boba Cafe Roblox 📰 This Reading Light App Will Revolutionize Your Nighttime Readingheres Why 9544439 📰 This Explosive Umco Stock Price Move Will Change Your Investment Strategy 165396 📰 Reagan Danielle Gray 7292332 📰 Calicivirus In Cats 8094511 📰 Angry Birds Two Game 8170376