To solve for the total number of 12 – flag signals Sally
can make, we need to make use of the formula:
total flags = d! / (a! b! c!)
Where,
d = is the number of flags to create a signal = 12
a = number of red flags = 5
b = number of green flags = 3
c = number of white flags = 4
We can observe from the equation that the individual
number of flags is factored out (or divided from) that is because all the 5 red
flags are similar, all the 3 flags are similar and all 4 flags are similar.
Going back into the equation, by substituting and
calculating:
total flags = 12! / (5! 3! 4!)
total flags = 27,720
<span>Therefore there are about 27,720 different 12-flags
signals.</span>
