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

Mathematics

Piper Valenzuela

9 April, 15:25

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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Cristina Powell · 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