Question:
The number of ways of arranging the letters of the word "EAPCET" is:
The number of ways of arranging the letters of the word "EAPCET" is:
Show Hint
Always check for repeating letters and divide by their factorials to prevent overcounting. Here, $\frac{6!}{2!} = 360$.
Updated On: May 31, 2026
- $360$
- $720$
- $180$
- $120$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The number of permutations of $n$ objects, where $p_1$ objects are of one kind, $p_2$ of another, is given by the formula: \[ P = \frac{n!}{p_1! \cdot p_2!} \]
Step 2: Meaning
We analyze the letters of the word "EAPCET". It has 6 letters, where the letter 'E' is repeated twice.
Step 3: Analysis
Count of letters:
• Total letters, $n = 6$
• Repeated letter 'E', $p_1 = 2$ Substitute into the permutation formula: \[ P = \frac{6!}{2!} = \frac{720}{2} = 360 \]
Step 4: Conclusion
The letters of the word "EAPCET" can be arranged in $360$ distinct ways. Final Answer: (A)
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