If there are 6 students and one is selected for best student and another is selected for runner up, then 15 different ways that we can arrange the students
Total number of students in the class = 6 students
Number of students for best student = 1 student
Number of students for runner up = 1 students
Total number of students needed = 2
Here we have to use the combination
6[tex]C_2[/tex] = 6! / 2!(6 - 2)!
= 6! / 2! × 4!
Split the terms and cancel it
= 6 × 5 / 2 × 1
Multiply the terms
= 30 / 2
Divide the numbers
= 15 combinations
Therefore, there are 15 combinations
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