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Problem Solving : Permutation and combination Problem 3: If the letter of the word SEQUESTERED are arranged in all possible ways and these words are written out as in a dictionary form, then what is the 50th rank of the word SEQUESTERED is ?

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If the letter of the word SEQUESTERED are arranged in all possible ways and these words are written out as in a dictionary form, then what is the 50th rank of the word SEQUESTERED is ?

Solution:

So the word SEQUESTERED can be arranged in dictionary form of letters as D E E E E Q R S S T U

Hence the number of words begin with DEEEEQR = 4! / 2! =12

and the number of words begin with DEEEEQS = 4! =24
the number of words begin with DEEEEQT = 4! / 2! =12

12+24+12 =48

so next word U becomes last word

hence next words are 49 and 50 will  be

DEEEEQURSST is 49th word

and DEEEEQURSTS is the 50th word

and the answer --> 50th rank of the word SEQUESTERED is "DEEEEQURSTS "

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