Select the correct answer. A student club has 15 members. How many ways can a committee of 6 members be chosen? A. 504 B. 720 C. 5,005 D. \( 3,603,600 \)

To solve this problem, we need to find how many ways we can choose 6 members from a group of 15. This is a combination problem, specifically denoted as \( C(n, k) = \frac{n!}{k!(n-k)!} \), where \( n \) is the total number of members, and \( k \) is the number of members to choose. Using this formula: \[ C(15, 6) = \frac{15!}{6! \times (15-6)!} = \frac{15!}{6! \times 9!} = \frac{15 \times 14 \times 13 \times 12 \times 11 \times 10}{6 \times 5 \times 4 \times 3 \times 2 \times 1} = 5,005 \] So, the correct answer is C. 5,005. For something a bit more fun, did you know that the concept of combinations goes back to ancient mathematics? In fact, the famous mathematician Pascal and his triangle were crucial for understanding binomial coefficients, which relate to combinations. Integer combinations, often visualized through enchanting patterns like the Pascal's Triangle, are not just numbers but tell stories of possibilities! Also, if you're interested in the world beyond math, the concept of combinations applies to various fields! From creating unique recipes to forming teams in sports, the number of ways we can combine elements affects our everyday decisions. So, next time you're choosing toppings for your pizza or selecting a movie night lineup, remember you’re employing the very same mathematical principles!