SOLUTION: How many times can the word "DEFENSE" be arranged using permutation or combination? And which one do you use?

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Question 314210: How many times can the word "DEFENSE" be arranged using permutation or combination? And which one do you use?
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) (Show Source):
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How many times can the word defense be arranged using permutation or combination?
And which one do you use?
Combinations is a count of groups.
Permutations is a count of arrangements.
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Arrangements of the word "defense"
Note: There are 3 "e"'s.
# of permutations = 7!/3! = 7*6*5*4 = 840
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Cheers,
Stan H.
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Answer by Edwin McCravy(20056) (Show Source):
You can put this solution on YOUR website!

If the three E's were colored difference, like this DEFENSE, the answer would be 7P7 or 7! since there are 7 letters. However, for example take the arrangement: SNEFEED If the E's were colored differently and we could tell the difference then we could rearrange the colored E's around and the following 6 would all be different: SNEFEED SNEFEED SNEFEED SNEFEED SNEFEED SNEFEED The reason there are 6 is because there are 3P3 = 3! ways the E's can be rearranged as above. So the answer 7! = 5040 is too large a numbee because every arrangement is counted 3! = 6 times too many. So we must divide 7! by 3! to get the correct answer. So the answer is Edwin