Multiple choice

How many different words can be formed using the letters of the word 'TEXTBOOK'?

  1. $10240$
  2. $10120$
  3. $10080$
  4. $8!$
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C Correct answer
Explanation

Word 'TEXTBOOK' has 8 letters: T(2), E(1), X(1), B(1), O(2), K(1). Total permutations = 8! / (2! * 2!) = 40320 / 4 = 10080.

AI explanation

The word TEXTBOOK consists of 8 letters, where T is repeated twice and O is repeated twice. Using the permutation formula for a multiset with repetitions, the total number of arrangements is 8 factorial divided by the product of the factorials of the counts of the identical letters. Therefore, the number of words is 8 factorial divided by (2 factorial times 2 factorial). Calculating this gives 40320 divided by 4, which equals 10080. The result is 10080.

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