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- Solution: The total ways to select 4 items: $\binom{25}{4} = 12650$. The unfavorable case (no turtles) is $\binom{15}{4} = 1365$. The probability of at least one turtle is $1 - \frac{1365}{12650} = 1 - \frac{273}{2530} = \frac{2257}{2530}$. The answer is $\boxed{\dfrac{2257}{2530}}$.
- Question: A student designs a bridge with 5 red struts and 7 blue connectors. If all struts and connectors are placed in a line, how many distinct sequences are possible if struts of the same color are indistinct?
- Solution: The total items are $5 + 7 = 12$, with 5 red and 7 blue. The number of distinct sequences is $\frac{12!}{5!7!} = 792$. Therefore, the answer is $\boxed{792}$.Question: A robotic engineer is programming a machine to assemble components using exactly 3 different colored
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