Respuesta :
Answer:
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.
The number of ways should be [tex]n!^2 ways[/tex]
The following information should be considered:
- To see why this is, each group must contain one of each student, which is [tex](n!)\times (n!)\times (n!)[/tex]ways to sort the students into groups.
- But, the order of the groups doesn't matter, so we have to divide by (n!), which is the number of ways to order the groups, leaving [tex](n!)^2[/tex] as the number of ways.
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