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  • How many different ways are there to arrange the letters in "ECCENTRICITY"?  Option: 1 8486400

How many different ways are there to arrange the letters in "ECCENTRICITY"?

 

Option: 1

8486400


Option: 2

7345600


Option: 3

8379200

 


Option: 4

9979200


Answers (1)

best_answer

Given that,

The given word is “ECCENTRICITY”.

The total number of letters in the word is 12.

The letter E is repeated twice.

The letter C is repeated thrice.

The letter T is repeated twice.

The letter I is repeated twice.

Thus, the number of ways the letters in the word are arranged is given by,

\begin{aligned} & \frac{12 !}{2 ! 3 ! 2 ! 2 !}=\frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2}{2 \times 3 \times 2 \times 2 \times 2} \\ & \frac{12 !}{2 ! 3 ! 2 ! 2 !}=12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 3 \times 5 \\ & \frac{12 !}{2 ! 3 ! 2 ! 2 !}=9979200 \end{aligned}

Therefore, the total number of ways the letters are arranged is 9979200 ways.

 

 

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Gunjita

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