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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? 📰 Double Crochet Stitch Youve Missed Turn Simple Rows Into Breathtaking Design 4025968 📰 Free Games App 1674489 📰 X Backbone Revealed What Hidden Power Really Gives Xbox Gamers The Edge 5148568 📰 Chilis Dessert 23928 📰 Mcdavid Stats 6253406 📰 Orange High School 3280188 📰 Long Neck Dinosaur 5562744 📰 Pure Peptides 6388279 📰 Game Store Download 4392779 📰 Microsoft Consulting Services You Need To Hiresave Your Company Thousands 9587105 📰 Sonic Advance This Secret Feature Will Blow Your Mind Dont Miss It 8176161 📰 From Laughter To Legacy Peter Griffins Ultimate Death Pose Confirmed 4668942 📰 Acidotic Respiration 4803830 📰 Gggolf Revealed The Secret Trick Pro Players Cant Stop Talking About 6181888 📰 Most Scary Horror Games 6019089