Question

The number of ways of arranging the letters of the word "EAPCET" is:

• A. $360$
• B. $720$
• C. $180$
• D. $120$

Hint:

Always check for repeating letters and divide by their factorials to prevent overcounting. Here, $\frac{6!}{2!} = 360$.

Answer 1

The Correct Option is A

Step 1: Count the letters.
The word is EAPCET. Listing the letters: E, A, P, C, E, T. That is $6$ letters in total.

Step 2: Spot the repeats.
Look for letters that appear more than once. The letter E appears twice. All the others appear once.

Step 3: Recall the formula.
When some letters repeat, the number of distinct arrangements is $\frac{n!}{p!}$, where $n$ is the total and $p!$ accounts for the repeated letter.

Step 4: Plug in the numbers.
Here $n = 6$ and the E repeats twice, so we divide by $2!$.
\[ \frac{6!}{2!} \]

Step 5: Work out the factorials.
We know $6! = 720$ and $2! = 2$.
\[ \frac{720}{2} = 360 \]

Step 6: State the answer.
So the letters can be arranged in $360$ different ways.
\[ \boxed{360} \]