GED Math: Combinations Word Problem - Forming a Committee of Men

Understanding Combinations Problems

• 🎯 When forming teams or committees, the order of selection does not matter, indicating a combinations problem.
• 💡 This is because selecting individuals like John, Kim, and Sally is the same as selecting Sally, Kim, and John for the same group.

Calculating the Number of Men

• 📊 The club has a total of 23 members, with 13 identified as women.
• 🧠 To find the number of men, subtract the number of women from the total members: 23 - 13 = 10 men.

Solving the Committee Selection

• 🔑 The problem requires forming a committee of four men from the available group of 10 men.
• 🧩 This is calculated using the combinations formula, denoted as 10C4, which represents selecting 4 items from a set of 10 where order is irrelevant.
• 🚀 The calculation involves factorials: 10! / (10-4)! * 4! = 10! / 6! * 4!.
• ✅ After simplification and cancellation (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1), the result is 210 different ways to form the committee.