Question

your class is holding elections to choose a leadership committee of 4 students. if there are 30 students in the class, how many different leadership committees would it be possible to elect? (1 point) 810,000 120 27,405 657,720

Explanation:

Step1: Determine the combination formula

The formula for combinations is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n\) is the total number of items, and \(r\) is the number of items to be chosen. Here, \(n = 30\) and \(r=4\).

Step2: Calculate factorial values

\(n!=30! = 30\times29\times28\times27\times26!\), \(r!=4!=4\times3\times2\times1 = 24\), and \((n - r)!=(30 - 4)!=26!\)

Step3: Substitute into the combination formula

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Answer:

27,405