Batuhanrelly3idn
Answered

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solve the problem completely
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?​

Sagot :

AGboiiidn

[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:

  • Given that n=7 r=3

[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]

  • There are 210 ways