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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
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B
692
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C
698
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D
616
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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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