Multiple choice

In how many different ways can the letter of the word FINANCE be arranged?

  1. $5040$
  2. $2040$
  3. $2520$
  4. $4080$

  5. None of these
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C Correct answer
Explanation

The word FINANCE has 7 letters, with N appearing twice. The number of arrangements is 7! / 2! = 5040 / 2 = 2520.

AI explanation

The word FINANCE contains 7 letters in total, with the letter N appearing twice and no other repetitions. To find the number of distinct arrangements, we use the permutation formula for a multiset, dividing the factorial of the total number of letters by the factorial of the number of repetitions. The calculation is 7! divided by 2!, which equals 5040 divided by 2. The total number of different ways the letters can be arranged is 2520.

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