SOLUTION: Signals are sent from a battleship by placing four flags on a vertical pole. How many different signals can be formed by selecting the four flags from 1. Four different colore

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Question 48480: Signals are sent from a battleship by placing four flags on a vertical pole. How many different signals can be formed by selecting the four flags from
1. Four different colored flags
2. Two different red flags & two identical white flags
Answer by longjonsilver(2297)   (Show Source): You can put this solution on YOUR website!
1 4 different red flags:
first flag: 4 possibles
second flag: 3 possibles (since one has been chosen as the first flag)
third flag: 2 possibilities
fourth flag: 1 possible flag.

Total: 4*3*2*1 --> 24 possible ways

2. 2 different red flags (r and R) and 2 identical white flags (W and W)

Permutations are, in order:
rRWW
rWRW
rWWR
RrWW
RWrW
RWWr
WWrR
WWRr
WrRW
WRrW
WrWR
WRWr

so answer is 12. Now algebraically we get this by starting with the 24 as the answer for 4 different flags and then dividing by 2! since we have 2 identical flags (the white ones):

24/2!
24/2
12

Hope this is clear.

jon.
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