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Home » Thus, number with **at least one** "33" is $ 64 - 21 = 43 $ - AMAZONAWS

Thus, number with **at least one** "33" is $ 64 - 21 = 43 $ - AMAZONAWS

📅 March 11, 2026 👤 scraface
Mar 11, 2026
Thus, number with **at least one** "33" is $ 64 - 21 = 43 $

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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?
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