Let's break down the expression \(\frac{\binom{5}{35} \cdot \binom{4}{55}}{706252528630}\) step by step:

1. **Combinations:**

   - \(\binom{5}{35}\) represents the number of ways to choose 5 objects from 35. It is calculated as:

   \[
   \binom{5}{35} = \frac{35!}{5!(35-5)!} = \frac{35!}{5!30!}
   \]

   - \(\binom{4}{55}\) represents the number of ways to choose 4 objects from 55. It is calculated as:

   \[
   \binom{4}{55} = \frac{55!}{4!(55-4)!} = \frac{55!}{4!51!}
   \]

2. **Multiplication of the combinations:**

   We will calculate the product of \(\binom{5}{35}\) and \(\binom{4}{55}\).

3. **Final division:**

   The final step is to divide this product by \(706252528630\).

I will calculate the result of this expression now.The result of the expression \(\frac{\binom{5}{35} \cdot \binom{4}{55}}{706252528630}\) is approximately \(0.1568\).

Would you like further details or explanations on any part of the calculation?

Here are 5 related questions for further exploration:
1. How are binomial coefficients related to probability theory?
2. What are some real-life applications of combination formulas?
3. How does the combination formula differ from permutations?
4. Can you explain the difference between independent and dependent events in probability?
5. What are factorials, and why are they important in combinatorics?

**Tip:** When solving combination problems, it's helpful to factorize large factorials to simplify calculations efficiently.

The query submitted by the user: (С(5, 35) * C(4, 55))/706252528630

Discover how to solve the mathematical expression (C(5, 35) * C(4, 55))/706252528630 by applying combination formulas and factorials. This step-by-step explanation covers core concepts in combinatorics and binomial coefficients, making it ideal for students at Grades 11-12 and college level.

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