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  • In how many ways can the letters of the word “ASSOCIATION” be arranged?  Option: 1 2494800<div class='qna-op

In how many ways can the letters of the word “ASSOCIATION” be arranged?

 

Option: 1

2494800


Option: 2

2294800


Option: 3

2394800


Option: 4

2594800


Answers (1)

best_answer

The given word is ASSOCIATION.

The letter ‘A’ is repeated 2 times.

The letter ‘S’ is repeated 2 times.

The letter ‘O’ is repeated 2 times.

The letter ‘I’ is repeated 2 times.

So, the number of ways to arrange the given word is given by,

\frac{11 !}{2 ! 2 ! 2 ! 2 !}=\frac{11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 2 \times 1 \times 2 \times 1 \times 2 \times 1}

Simplifying the terms to get,

\frac{11 !}{2 ! 2 ! 2 ! 2 !}=2494800

Therefore, the number of ways the word is arranged is 2494800.

 

 

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