Question

Find the rank of the word ZENITH.
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Answer 1

$\large\underline{\sf{Solution-}}$

We have to find the rank of the word ZENITH. So, first rearrange the alphabets of the word ZENITH in accordance to dictionary order.

E, H, I, N, T, Z

Now,

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c}\sf Word \: starting \: with&\sf Total \: words\:\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}\\\sf {E}&\sf {5! = 120} \: \\ \\\sf {H}&\sf {5! = 120} \\ \\\sf {I}&\sf {5! = 120}\\ \\ \sf {N}&\sf {5! = 120} \\ \\\sf {T}&\sf {5! = 120} \\ \\\sf {ZEH}&\sf {3! = 6} \\ \\\sf {ZEI}&\sf {3! = 6} \\ \\\sf {ZENH}&\sf {2! = 2} \\ \\\sf {ZENIH}&\sf {1! = 1} \\ \\\sf {ZENITH}&\sf {1} \\ \\\sf & \sf & \\\frac{\qquad}{ \sf \: Rank \: of \: ZENITH}&\frac{\qquad}{ \sf \: 616}\end{array}}\end{gathered}\end{gathered}\end{gathered}$

Hence, Rank of the word ZENITH is 616.