Question

# The letters of word 'ZENITH' are written in all positive ways. If all these words are written in the order of a dictionary, then the rank of the word 'ZENITH' is

A
716
B
692
C
698
D
616

Solution

## The correct option is D $$616$$The total number of words is $$6! = 720$$. Let us write the letters of word ZENITH alphabetically, i.e, EHINTZ.For ZENITH word starts withWord starting withNumber of words$$Z$$$$E$$$$5!$$$$H$$$$5!$$$$I$$$$5!$$$$N$$$$5!$$$$T$$$$5!$$ZENZEH$$3!$$ZEI$$3!$$ZENIZENH$$2$$ZENITZENIH$$1$$Total number of words before ZERNITH$$615$$Hence, there are $$615$$ words before ZENITH, so the rank of ZENITH is $$616$$.Mathematics

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