## monroe17 3 years ago Professor Bartlett teaches a class of 11 students. She has a visually impaired student, Louise, who must sit in the front row next to her tutor, who is also a member of this class. Assume that the front row has eight 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?

1. monroe17

@jim_thompson5910 help? :)

2. jim_thompson5910

A big key phrase here is that "the tutor must be seated to the right of Louise", so if T is the tutor and L is Louise, then you can only have LT and NOT TL So basically LT is one person since you can't a) separate the two AND b) you can't reorder it

3. monroe17

so 6 spaces left right

4. jim_thompson5910

So instead of 11 students to order, you really have 11-2+1 = 10 students to order since you're combining two students to form one "student'

5. monroe17

10P6 maybe?

6. jim_thompson5910

There are 8 chairs in the front, but 2 are taken up and combined into one "chair" so to speak. So there are really 8-2+1 = 7 "chairs" in the front row.

7. jim_thompson5910

So it's really 10 P 7

8. monroe17

so 10P7?

9. jim_thompson5910

you got it

10. monroe17

5040 ways?

11. jim_thompson5910

5040 is 7! or 7 P 7, so no

12. monroe17

whats 10P7 then?

13. jim_thompson5910

10 P 7 = (10!)/((10-7)!)

14. monroe17

604800= (10!)/(3!)?

15. jim_thompson5910

you got it

16. monroe17

finally thank you!

17. jim_thompson5910

you're welcome