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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 \binom{7}{3} \cdot \binom{9}{2}

📌 Compute the values:

📌 \binom{7}{3} = 35,\quad \binom{9}{2} = 36,\quad \binom{16}{5} = 4368

📌 \frac{35 \cdot 36}{4368} = \frac{1260}{4368}

📌 \frac{1260}{4368} = \frac{105}{364}

📌 Thus, the probability is $\boxed{\frac{105}{364}}$.

📌 Question: How many 8-digit positive integers composed only of the digits 3 and 4 contain at least one instance of two consecutive 3s?

📌 Solution: First, compute the total number of 8-digit numbers using only digits 3 and 4:

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📝 Recent Posts

#### 314
Question**: Solve the quadratic equation \( 2x^2 - 5x - 3 = 0 \) using...
The quadratic formula is \( x = rac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).
Here, \( a = 2 \), \( b = -5 \), \( c = -3 \).
Discriminant: \( \Delta = (-5)^2 - 4(2)(-3) = 25 + 24 = 49 \).
\( x = rac{-(-5) \pm \sqrt{49}}{2(2)} = rac{5 \pm 7}{4} \).
So, \( x = rac{5 + 7}{4} = 3 \) or \( x = rac{5 - 7}{4} = -0.5 \).
The solutions are \( x = 3 \) and \( x = -0.5 \).
#### 3, -0.5
Question**: A train travels 300 km in 4 hours. If it increases its spe...

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