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
Let us arrange the letters of the word ZENITH in the alphabetical order.
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 _ _ _ _ _ →5P5 = 5! words
H _ _ _ _ _→5P5 = 5! words
I _ _ _ _ _→5P5 = 5! words
N _ _ _ _ _→5P5 = 5! words
T _ _ _ _ _→5P5 = 5! words
Z E H _ _ _→3P3 = 3! words
Z E I _ _ _ →3P3 = 3! words
Z E N H _ _→2P2 = 2! words
Z E N I H →1P1 = 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 = 5×5!+2×3!+2!+1 = 615
Since there are 615 words before ZENITH, rank of the word ZENITH = 616