Question

The number of distinct arrangements of the letters of the word STATISTICS is:

• A. 50,400
• B. 25,200
• C. 12,600
• D. 5,040

Hint:

For word permutations, always divide by the factorials of repeated letters to avoid overcounting.

Answer 1

The Correct Option is A

Step 1: Count the total number of letters.
The word STATISTICS contains 10 letters in total.
Step 2: Identify repeated letters.
S appears 3 times.
T appears 3 times.
I appears 2 times.
A and C appear once each.
Step 3: Apply the formula for permutations with repetition.
The number of distinct arrangements is given by:
\[ \frac{10!}{3! \times 3! \times 2!} \]
Step 4: Simplify the expression.
\[ \frac{10!}{3! \times 3! \times 2!} = \frac{3628800}{72} = 50,400 \]
Step 5: Conclusion.
The total number of distinct arrangements of the letters of the word STATISTICS is 50,400.