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Home » \( \binom82 = \frac8 \times 72 = 28 \) - go-checkin.com

\( \binom82 = \frac8 \times 72 = 28 \) - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Number of ways to choose 3 revolutions excluding the top 2 (i.e., choosing all 3 from the remaining 8):

📌 So, the probability that neither of the top 2 is selected is:

📌 \frac{56}{120} = \frac{7}{15}

📌 Therefore, the probability that at least one of the top 2 is selected is:

📌 - \frac{7}{15} = \frac{8}{15}

📌 \boxed{\frac{8}{15}}

📌 Question: A food scientist is developing a new low-sugar snack bar and tests 10 different formulations. If she randomly selects 3 for nutritional analysis, what is the probability that at least two of them are among the top 4 most promising candidates?

📌 We calculate the probability of selecting **exactly 2** or **exactly 3** of the top 4 formulations, and sum them.

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So total favorable sequences:
$4 \times 3 \times 12 = 144$
Therefore, the desired probability is:
\frac{144}{256} = \frac{9}{16}
Wait — but this counts only sequences with one pair and two singles, a...
But note: the problem says exactly two of the chosen options are the s...
Thus, our count is correct.
Hence, the probability is:
But wait: $144 \div 16 = 9$, $256 \div 16 = 16$, yes: $\frac{144}{256}...
Wait: $144 / 16 = 9$, $256 / 16 = 16$, so yes, $\frac{144}{256} = \fra...

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