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Home » Therefore, the population approaches \(\boxed500\) as \( t \to \infty \). - Midis

Therefore, the population approaches \(\boxed500\) as \( t \to \infty \). - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 #### 16**Question:

📌 A science policy analyst is reviewing the distribution of grants for three categories of projects: renewable energy, AI research, and public health. There are 5 grants for renewable energy, 7 for AI research, and 3 for public health. If a committee randomly selects 3 grants to review, what is the probability that exactly 2 are for AI research and 1 is for public health?

📌 To solve this problem, we need to calculate the probability of selecting exactly 2 AI research grants and 1 public health grant out of the total grants.

📌 First, calculate the total number of grants:

📌 \[ 5 + 7 + 3 = 15 \]

📌 Next, calculate the number of ways to choose 2 AI research grants from 7:

📌 \[ \binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21 \]

📌 Then, calculate the number of ways to choose 1 public health grant from 3:

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Note \(888 \mod 125 = 888 - 7\cdot125 = 888 - 875 = 13\), so:
n^3 \equiv 13 \pmod{125}
We search for a solution to \(n^3 \equiv 13 \pmod{125}\). Try lifting...
Try small values modulo 5 first:
Mod 5: \(n^3 \equiv 13 \equiv 3 \pmod{5}\)
Check cubes mod 5:
\(0^3 = 0\)
\(1^3 = 1\)
\(2^3 = 8 \equiv 3\)
\(3^3 = 27 \equiv 2\)

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