Question

Find the number of words formed by permuting all the letters of the word INDEPENDENCE.

• A. 144
• B. 1663200
• C. 136050
• D. 6432
• E. 720

Hint:

For word permutations with repeated letters, divide total factorial by factorials of each repetition count.

Answer 1

The Correct Option is B

Step 1: Count total letters.
Word = INDEPENDENCE → 12 letters.

Step 2: Frequency of repetitions.
I – 1, N – 3, D – 2, E – 4, P – 1, C – 1.

Step 3: Formula for permutations with repetitions.
\[ \frac{12!}{3! \cdot 2! \cdot 4!} \]
Step 4: Calculate.
\[ 12! = 479001600 \] Denominator = \(3! \times 2! \times 4! = 6 \times 2 \times 24 = 288\).
So total = \(\dfrac{479001600}{288} = 1663200\).

Final Answer:
\[ \boxed{1663200} \]