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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? 📰 Phys Stock Price Shock Did This Shocking Breakthrough Spike Shares To New Heights 215621 📰 Hemos 2036926 📰 Heavy Cream Nutrition 4817819 📰 Nutritional Value In Tilapia 1575091 📰 These Mini Tacos Are So Small Theyll Change How You Eat Forevertry Them Now 8109416 📰 Puzzle Bobble The Mind Blowing Hack To Solve Any Level Instantly 9813010 📰 Arab Saudi Currency 1144645 📰 When Does Dq Open 4065885 📰 Pease Golf 2693489 📰 Boot A Pendrive Like A Pro The Hidden Trick That Works Every Time 5810549 📰 You Wont Believe What Happens When You Enter The Kingdom Redyoull Never Leave 2520958 📰 Patricia Gucci 6188449 📰 4 Unlock Your Usb Forever The Shocking Way To Remove Protection 6321567 📰 Puerto Rico Trip 6670685 📰 These Violent Games With Guns Are Taking Over Playlistsare You Ready 7339115