In how many ways can the letters of the word ACCEPTANCE be arranged?

  • A 10! / (2!2!3!)
  • B 10! / ( 2!3!)
  • C 10! / (2!2!)
  • D 10!
jamb 2008mathematics

The correct answer is A. 10! / (2!2!3!)

The word ACCEPTANCE has 10 letters, with 2 A's, 2 C's, and 3 E's. The number of ways to arrange n objects, where some objects are identical, is given by the formula n! / (p1! p2! ... pk!), where p1, p2, ..., pk are the frequencies of the identical objects. In this case, the number of ways to arrange the letters of the word ACCEPTANCE is 10! / (2! 2! 3!).

So, the correct answer is 10! / (2!2!3!).

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