[tex] \large\underline \mathcal{{QUESTION:}}[/tex]
Suppose we have 7 potted plants and we wish to arrange 3 of them in a row. in how many ways can this be done?
[tex]\\[/tex]
[tex] \large\underline \mathcal{{SOLUTION:}}[/tex]
Using the Linear Permutation Formula:
[tex]\sf{P(n,r)=\frac{n!}{(n-r)!}}[/tex]
[tex]\sf{P(7,3)=\frac{7!}{(7-3)!}}[/tex]
[tex]\sf{P(7,3)=\frac{7!}{4!}}[/tex]
[tex]\sf{P(7,3)=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1}}[/tex]
[tex]\sf{P(7,3)=\frac{7 \times 6 \times 5 \times \cancel{4 \times 3 \times 2 \times 1}}{ \cancel{4 \times 3 \times 2 \times 1}}}[/tex]
[tex]\sf{P(7,3)=7\times6\times5}[/tex]
[tex]\sf{P(7,3)=210}[/tex]
[tex]\\[/tex]
[tex] \large\underline \mathcal{{ANSWER:}}[/tex]
