A class is attended by n sophomores, n juniors, and n seniors. In how many ways can these students form n groups of three people each if each group is to contain a sophomore, a junior, and a senior

n!² ways

Step-by-step explanation:

The number of ways in which the students can form "n" groups of three people each provided that each group has to contain a sophomore, a junior, and a senior inclusive.

The first step to take is to line up the sophmores in any and no particular way. After doing that, we proceed to lining up the juniors across from the sophmores in any one of n! ways. Finally, we get to line up the seniors across from the juniors in any one of n! ways.

After all these we get a result that is a total of n!² ways.

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: