1) For choosing an entrance we have $\binom{6}{1}$ choices, and for corresponding exits, we have$\binom{5}{1}$ choices. So total ways = 6 * 5 = 30 2) Rainbow has 7 colors. We need 3 colors to form a tricolor flag. So total tricolor flags possible = $\binom{7}{3}$ * 3! = 210

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Aptitude Overflow