The king has 11 (different) colored flags that he uses to send coded messages to his general in the field. For example, blue-green-red-white might mean "attack at dawn" and white-red-green-blue may mean "retreat." He sends the message by arranging four of the flags atop the castle wall. How many coded messages can the king sent?

Question

Viviana

Mathematics

10 August, 06:01

The king has 11 (different) colored flags that he uses to send coded messages to his general in the field. For example, blue-green-red-white might mean "attack at dawn" and white-red-green-blue may mean "retreat." He sends the message by arranging four of the flags atop the castle wall. How many coded messages can the king sent?

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Answers (1)

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Zachary Rangel · Answer 1

V₁₁,₄ = 7920

Step-by-step explanation:

Mssages from the King need of the adecuate sequence that means

blue-green-red-white and white - red - green-blue are differents messages therefore we are in presence of a vaiations problem

V₁₁,₄ = 11! / (11-4) !

V₁₁,₄ = 11! / 7! ⇒ V₁₁,₄ = 11*10*9*8*7!/7! V₁₁,₄ = 11*10*9*8

V₁₁,₄ = 7920