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permutations

by Ozlemg » Fri Jun 24, 2011 5:41 am
Let each different arrangement of all the letters of DELETED be called a word.

(a) How many words are possible?

(b) In how many of these words will the D's be separated?

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by Frankenstein » Fri Jun 24, 2011 5:47 am
Hi,
DELETED has 2Ds,3Es,1L,1T
a) Number of words is 7!/(2!.3!) = 420
b) If both Ds are together then we take that pair as a separate entity say P
So, we have 3Es,1L,1T,1P
Number of words with both Ds together is 6!/3! = 120
So, words in which 2Ds are separated is 420-120 = 300.
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