Question

a class has 30 students. in how many different ways can five students form a group for an activity? (assume the order of the students is not important.) there are different ways that the five students can form a group for an activity. (type a whole number.)

Explanation:

Step1: Use combination formula

The combination formula is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 30\) (total number of students) and \(r=5\) (number of students in a group).

Step2: Calculate factorial values

\(n!=30! = 30\times29\times28\times27\times26\times25!\), \(r!=5!=5\times4\times3\times2\times1 = 120\), and \((n - r)!=(30 - 5)!=25!\)

Step3: Substitute into the formula

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Step4: Simplify the expression

$$
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Answer:

\(142506\)