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There are 15 students in a social studies class. Two students will be selected to present their term projects today. In how many different orders can two students be selected?

Verified Answer :

meerkat18

Given:
15 students
2 students must be chosen.
No repetition, no order

This is a combinations problem. We use this formula: n! / (n-r)!(r!)

n = 15 ; r = 2

15! / (15-2)!(r!) ⇒ 15! / 13! * 2! = 105

Using the combination formula, it is found that the students can be selected in 105 ways.

The order in which the students are selected is not important, hence the combination formula is used to solve this question.

What is the combination formula?

The number of possible combinations of x elements from a set of n elements is given by:

\(C_{(n,x)} = \frac{n!}{x!(n-x)!}\)

In this problem, two students are selected from a set of 15, hence the number of different orders is given by:

\(C_{15,2} = \frac{15!}{2!13!} = 15 \times 7 = 105\)

More can be learned about the combination formula at https://brainly.com/question/25821700

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