[tex] \large\underline \mathcal{{QUESTION:}}[/tex]
In how many different ways can 11 people occupy the 11 seats in a back row of a mini theater?
[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(11,11)=\frac{11!}{(11-11)!}}[/tex]
[tex]\sf{P(11,11)=\frac{11!}{0!}}[/tex]
[tex]\sf{P(11,11)=\frac{11\times10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{1}}[/tex]
[tex]\sf{P(11,11)=39,916,800}[/tex]
[tex]\\[/tex]
[tex] \large\underline \mathcal{{ANSWER:}}[/tex]
- There are 39,916,800 ways
