[tex] \large\underline \mathcal{{QUESTION:}}[/tex]
If P(9,r)= 3024, what is r?
[tex]\\[/tex]
[tex] \large\underline \mathcal{{SOLUTION:}}[/tex]
- [tex]\sf{P(9,r)=3024}[/tex]
[tex]\sf{P(n,r)=\frac{n!}{(n-r)!}}[/tex]
[tex]\sf{3024=\frac{n!}{(n-r)!}}[/tex]
[tex]\sf{3024=\frac{9!}{(9-r)!}}[/tex]
[tex]\sf{(9-r)!=\frac{362,880}{3024}}[/tex]
[tex]\sf{(9-r)!=120}[/tex]
[tex]\sf{(9-r)!=5!}[/tex]
[tex]\sf{9-r=5\:\implies 9-5=r \implies \boxed{\sf{4=r}}}[/tex]
[tex]\\[/tex]
[tex] \large\underline \mathcal{{ANSWER:}}[/tex]
