Multiple Choice
A student formed a club at their school. They have 13 members, and need to elect a president, vice president, and treasurer. How many ways are there to fill these officer positions?
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Multiple Choice
From a class of 28 students, in how many ways could a teacher select 4 students to lead the class discussion?
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Verified step by step guidance1
Identify the problem as a combination problem, where the order of selection does not matter.
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.
Substitute the values into the formula: n = 28 and k = 4. This gives us C(28, 4) = 28! / (4! * (28-4)!).
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.
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.
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