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In how many different ways can 11 people occupy the 11 seats in a back row of a mini theater?

Sagot :

[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

  • Given: n=11 , r = 11

[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

Question:

In how many different ways can 11 people occupy the 11 seats in a back row of a mini theater?

Answer:

39,916,800 ways

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