Solution: First, calculate the total number of ways to choose 5 opportunities from 8 without restrictions: $\binom85 = 56$. 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: $\binom63 = 20$. Thus, the valid portfolios are $56 - 20 = 36$. The final answer is $\boxed36$. - Abu Waleed Tea
Mar 01, 2026
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