Question

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?

Answer 1

V₁₁,₄ = 7920

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