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A debate team consists of five freshmen and four sophomores. (Everyone is distinguishable.) How many ways can they stand in line, so that at least two of the freshmen are standing next to each other

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Using the arrangements formula, it is found that they can stand in the line in 80,640 ways.

What is the arrangements formula?

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, we have that:

  • The 2 freshmen are in 2! positions, in any of the 8 positions from 1 to 8.
  • The other 7 students are arranged in 7! positions.

Hence the number of ways in which they can be lined up is given by:

N = 2! x 8 x 7! = 80,640.

More can be learned about the arrangements formula at https://brainly.com/question/25925367

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