Question 1191221
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How many signals can be made with 5 different flags by raising them any number at a time?
Show full solution, thank you!
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            As worded, this problem admits different readings, interpretations, solutions and answers.


            See my interpretation, different from that of the other tutor.


            I will assume that  5  flags are  NOT  ONLY  DIFFERENT  (they always are different),  but distinguished.

            More concretely and for clarity,  I will assume that the flags have different colors.



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By raising one flag at a time, I can make 5 different signals.


By raising two flags at a time, I can make 5*4 = 20 different signals 
    (if to read them from top to bottom, or from left to right).


By raising three flags at a time, I can make 5*4*3 = 60 different signals 
    (if to read them from top to bottom, or from left to right).


By raising four flags at a time, I can make 5*4*3*2 = 120 different signals 
    (if to read them from top to bottom, or from left to right).


By raising five flags at a time, I can make 5*4*3*2*1 = 120 different signals 
    (if to read them from top to bottom, or from left to right).


In all, I can make  5 + 20 + 60 + 120 + 120 = 325 different signals,
    by raising different number of distinguishable flags at a time.
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Solved &nbsp;(differently).