Multiple choice

The number of all possible different arrangement of the word $"BANANA"$ is

  1. $\lfloor 6  $
  2. $\lfloor 6  \times \lfloor 2 \times \lfloor 3 $
  3. $\dfrac {\lfloor 6 }{\lfloor 2 \times \lfloor 3 }$
  4. $none\ of\ these$
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C Correct answer
AI explanation

The word BANANA consists of 6 letters where the letter A repeats 3 times and the letter N repeats 2 times. To find the total number of distinct arrangements, we use the permutation formula for a multiset, dividing the factorial of the total number of letters by the factorials of the repeated letters. The calculation is 6! divided by the product of 3! and 2!. This matches the given option by representing the factorial of 6 divided by the factorial of 2 times the factorial of 3.

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