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Professor Bartlett teaches a class of 10 students. She has a visually challenged student, Louise, who must sit in the front row next to her tutor, who is also a member of the class. Assume that the front
row has seven chairs, and the tutor must be seated to the right of Louise How many different ways can Professor Bartlett assign students to sit in the first row?

Respuesta :

Using the permutation formula, it is found that Professor Bartlett can assign the students in 90,720 ways.

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The permutation formula states that the number of ways x elements from a set of n can be assigned is:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

  • For Louise and the tutor, there are 6 possible outcomes, seats 1-2, 2-3, 3-4, 4-5, 5-6 and 6-7.
  • For the remainder of the students, 5 are chosen from a set of 9, thus:

[tex]T = 6 \times P_{9,5} = 6 \times \frac{9!}{4!} = 90720[/tex]

The students can be assigned in 90,720 ways.

A similar problem is given at https://brainly.com/question/14632626

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