From a class of 28 students, in how many ways could a teacher select 4 students to lead the class discussion?

• A. 491,400
• B. 24
• C. 11,793,600
• D. 20,475

Answer: (D)

Verified step by step guidance

1. Identify that this is a combination problem, where order does not matter. We need to select 4 students from a total of 28.
2. Use the combination formula: \( C(n, r) = \frac{n!}{r!(n-r)!} \), where \( n \) is the total number of items to choose from, and \( r \) is the number of items to choose.
3. Substitute the values into the formula: \( C(28, 4) = \frac{28!}{4!(28-4)!} \).
4. Calculate \( 28! \), \( 4! \), and \( 24! \) separately. Remember that \( n! \) (n factorial) is the product of all positive integers up to \( n \).
5. Divide \( 28! \) by the product of \( 4! \) and \( 24! \) to find the number of combinations, which will give you the number of ways to select 4 students from 28.