Answer:
504 possible signals
Step-by-step explanation:
If all of the flags are distinguishable, there are 9 choices for the first position, 8 for the second, 7 for the third, and on down to one final choice for the last position. The total number of choices is ...
9·8·7·6·5·4·3·2·1 = 9! = 360,880
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However, there are 3 white flags that are indistinguishable. Those three flags can be in any of 3·2·1 = 6 different orders, wherever they might be in the signal. Hence, we must divide the number of different signals by 6 to account for the indistinguishable white flags:
362,880/6 = 60,480
Each of these signals has 5 red flags that are indistinguishable. Those can be in any of 5! = 120 different orders, wherever they are in the signal. Hence the total number of distinguishable signals is ...
60480/120 = 504
504 different signals can be made from the 9 flags.
