There are 2024 ways in which the instructor can choose 3 students from a class of 24 students for the field trip.
A combination is a mathematical technique for calculating the number of possible arrangements in a set of items where the order of the selection is unimportant.You can choose the items in any order in combinations.
Permutations and combinations are often confused. In permutations, however, the order of the selected items is critical. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), but different in permutations.
There is a way you can calculate combinations using a formula. This formula is:
[tex]nC_r = \frac{n! }{ r!(n-r)! }[/tex]
where
n = total no. of items;
r = items selected for the combination;
"!" is the factorial
Given,
Total number of students in class , n = 24
Number of students selected, r = 3
So, the number of ways that 3 students can be selected from 24 students is
[tex]24C_3=\frac{24 !}{3!(24-3) !}\\\\=\frac{24 !}{3!*21 !}\\\\=\frac{3!*24*23*22*21 !}{3!*21 !}\\\\=\frac{24*23*22}{3*2*1}\\\\=2024[/tex]
Hence, the students can be selected in 2024 ways for the field trip.
To learn more about combinations refer here
https://brainly.com/question/29212305
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