[tex] \large\underline \mathcal{{QUESTION:}}[/tex]
9. In a room, there are 8 chairs in a row. In how many ways can 6 students be seated in consecutive chairs?
- A. 2
- B. 720
- C. 20 160
- D. 21 060
[tex]\\[/tex]
[tex] \large\underline \mathcal{{SOLUTION:}}[/tex]
Using the linear permutation
[tex]\\[/tex]
[tex]\sf{P(n,r)=\frac{n!}{(n-r)!}}[/tex]
[tex]\sf{P(8,6)=\frac{8!}{(8-6)!}}[/tex]
[tex]\sf{P(8,6)=\frac{8!}{2!}}[/tex]
[tex]\sf{P(8,6)=\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1}}[/tex]
[tex]\sf{P(8,6)=\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times \cancel{2 \times 1}}{ \cancel{2 \times 1}}}[/tex]
[tex]\sf{P(8,6)=8 \times 7 \times 6 \times 5 \times 4 \times 3 } [/tex]
[tex]\sf{P(8,6)=20,160}[/tex]
[tex]\\[/tex]
[tex] \large\underline \mathcal{{ANSWER:}}[/tex]
[tex]\\[/tex]
[tex]\\[/tex]
To learn more about problems involving permutations: Visit this link
https://brainly.ph/question/13885772
