Question

The letters of the word ZENITH are permuted and are arranged in an alphabetical order as in an English dictionary.

Then, the rank of the word ZENITH is ___

Answer 1

Let us arrange the letters of the word ZENITH in the alphabetical order.

EHINTZ

In the dictionary, the words appearing first will begin with E, then H, then I, then N , then T and at last Z.

Let us fix the first position as E.

E _ _ _ _ _ $\to {}^5{P}_5$ = 5! words

H _ _ _ _ _$\to {}^5{P}_5$ = 5! words

I _ _ _ _ _$\to {}^5{P}_5$ = 5! words

N _ _ _ _ _$\to {}^5{P}_5$ = 5! words

T _ _ _ _ _$\to {}^5{P}_5$ = 5! words

Z E H _ _ _$\to {}^3{P}_3$ = 3! words

Z E I _ _ _ $\to {}^3{P}_3$ = 3! words

Z E N H _ _$\to {}^2{P}_2$ = 2! words

Z E N I H $\to {}^1{P}_1$ = 1! words

Z E N I T H comes in order after all the above words

So, number of words before Z E N I T H = $5\times 5!+2\times 3!+2!+1$ = 615

Since there are 615 words before ZENITH, rank of the word ZENITH = 616