Solution: The total number of ways to choose 3 sites from 10 is:
["Solution: The Total Number of Ways to Choose 3 Sites from 10", "When planning projects, research, or site selection in fields like real estate, business development, or academic studies, one common question arises: how many unique ways can we choose 3 sites from a total of 10? This is a fundamental problem in combinatorics, solved using combinations — a key mathematical concept with real-world applications.", "---", "### What Is a Combination?", "A combination refers to the number of ways to select items from a larger group where the order does not matter. In mathematical terms, the number of ways to choose k elements from a set of n elements is given by the combination formula:", "[\n\binom{n}{k} = \frac{n!}{k!(n - k)!}\n]", "---", "### Applying the Formula: Choosing 3 Sites from 10", "In our case, we want to find the total number of combinations when selecting 3 sites (k = 3) from 10 available sites (n = 10):", "[\n\binom{10}{3} = \frac{10!}{3!(10 - 3)!} = \frac{10!}{3! \cdot 7!}\n]", "We can simplify this by canceling out the common factorial terms:", "[\n\binom{10}{3} = \frac{10 \ imes 9 \ imes 8 \ imes 7!}{3! \ imes 7!} = \frac{10 \ imes 9 \ imes 8}{3 \ imes 2 \ imes 1}\n]", "[\n\binom{10}{3} = \frac{720}{6} = 120\n]", "---", "### Interpretation and Real-World Relevance", "This result means there are 120 distinct combinations of 3 sites that can be selected from a total of 10. Whether you're evaluating real estate portfolios, testing multiple locations for a business, or dividing study groups, understanding combinations helps make informed, data-driven choices without redundancy.", "---", "### Why This Matters", "- Efficiency: Combinatorics helps reduce computational complexity by avoiding duplicate selections.\n- Strategic Planning: Knowing the total number of combinations enables better resource allocation.\n- Mathematical Foundation: The concept underpins probability, statistics, and algorithm design.", "---", "### Conclusion", "The total number of ways to choose 3 sites from 10 is 120 — a powerful insight rooted in the elegant mathematics of combinations. Embracing this approach ensures clarity and precision in decision-making across diverse applications.", "---", "Tags: combinatorics, combinations, binomial coefficient, choose 3 from 10, mathematical formula, site selection, counting methods, real-world applications", "Meta Description: Discover the total number of ways to choose 3 sites from 10 using the combination formula. Learn why this calculation matters in project planning, business strategy, and data analysis."]
