Explanation

We need to choose a 4-student committee from a panel of 12 students. This is a combination problem, as the order of selection doesn't matter. We can use the combination formula:

C(n, k) = n! / (k!(n-k)!)

where n is the total number of students (12), k is the number of students to be chosen (4), and ! denotes the factorial function.

C(12, 4) = 12! / (4!(12-4)!)

= 12! / (4!8!)

= (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1)

= 495

So, there are 495 different ways to choose a 4-student committee from a panel of 12 students.