Q56 / 160 · TS EAMCET 2024 (10 May Shift 1) · Mathematics
All the letters of the word 'COLLEGE' are arranged in all possible ways and all the seven letter words (with or without meaning) thus formed are arranged in the dictionary order. Then the rank of the word 'COLLEGE' is
- A119
- B149
- C176
- Correct answerD179
Solution
COLLEGE
$\begin{array}{|c|c|c|c|c|c|c|}\hline 1 & 5 & 4 & 4 & 2 & 3 & 2 \\C & O & L & L & E & G & E \\\hline 6!\times 0 & \frac{5!\times 5}{2 \times 2} & \frac{4!\times 3}{2 \times 2} & \frac{3!\times 3}{2} & 2!\times 0 & 1!\times 1 & 0!\times 0 \\\hline\end{array}$
Then rank of college $\begin{aligned} & \text {Then rank of college } \\ & \begin{array}{l} =\left(\frac{5 \times 5!}{2 \times 2!}+\frac{4 \times 3}{2 \times 2!}+\frac{3 \times 3!}{2!}+1\right)+1=\left(\frac{600}{4}+18+9+1\right)+1 \\ =150+28+1=179 \end{array} \end{aligned}$
Then rank of college $\begin{aligned} & \text {Then rank of college } \\ & \begin{array}{l} =\left(\frac{5 \times 5!}{2 \times 2!}+\frac{4 \times 3}{2 \times 2!}+\frac{3 \times 3!}{2!}+1\right)+1=\left(\frac{600}{4}+18+9+1\right)+1 \\ =150+28+1=179 \end{array} \end{aligned}$
Hence, the correct answer is option: 'D'.