If all the seven letters of the word LEADING are permuted in all possible ways and the words thus formed are…

If all the seven letters of the word LEADING are permuted in all possible ways and the words thus formed are arranged as in the dictionary order, then the word in $2017^{\text {th }}$ place is
  1. ELIGDAN
  2. ELNADGI
  3. ELINADG
  4. ELNDAGI

Solution

When letters of LEADING are arranged in ascending order then letters are A, D, E, G, I, L, N Now, words starts with $\mathrm{A}$ is $6 !=720$, ie. $A$........ Similarly, words starts with $D=6 !=720$ Now, words starts with $E$ is also $6 !=720$. But total number is 2160 that is more than 2017th place. Hence, word will start with $E$. Now, words starts with $ \begin{aligned} & E A \ldots \ldots .=5 !=120 \\ & E D \ldots \ldots . .=5 !=120 \\ & E G \ldots \ldots . .=5 !=120 \\ & E I \ldots \ldots . .=5 !=120 \end{aligned} $ Here, total words till now is $720+480=1920$ Now, words start with $ \begin{aligned} & \text { ELA } \ldots \ldots \ldots=4 !=24 \\ & E L D \ldots \ldots .=4 !=24 \\ & E L G \ldots \ldots .=4 !=24 \\ & E L I \ldots \ldots . .=4 !=24 \end{aligned} $ Now, total words is 2016. Next word is 2017th word and the word is ELNADGI

Asked in: AP EAMCET 2018 (23 Apr Shift 1)

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