Sally has 5 red flags, 3 green flags, and 4 white flags. how many 12 -flag signals can she run up a flag pole

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

Therefore there are about 27,720 different 12-flags signals.