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. $20,475$

Answer: (C)

Verified step by step guidance

1. Identify the problem as a combination problem, where the order of selection does not matter.
2. Use the combination formula to determine the number of ways to select 4 students from 28. The formula is: C(n, k) = n! / (k! * (n-k)!), where n is the total number of students, and k is the number of students to be selected.
3. Substitute the values into the formula: n = 28 and k = 4. This gives us C(28, 4) = 28! / (4! * (28-4)!).
4. Simplify the expression: Calculate 28! / (4! * 24!). Since 24! is a common factor in both the numerator and the denominator, it can be canceled out, simplifying the calculation.
5. Calculate the remaining expression: 28 * 27 * 26 * 25 / (4 * 3 * 2 * 1). This will give you the number of ways to select 4 students from 28.