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  • How many different ways can the letters in the word "PARALLELOGRAM" be arranged?Option: 1 86486400  <di

How many different ways can the letters in the word "PARALLELOGRAM" be arranged?

Option: 1

86486400
 


Option: 2

76486300


Option: 3

84486400

 


Option: 4

76486400


Answers (1)

best_answer

Given that,
The given word is "PARALLELOGRAM".
The total number of letters in the word is 13.
The letter A is repeated thrice.
The letter R is repeated twice.
The letter L is repeated thrice.
Thus, the number of ways the letters in the word are arranged is given by,

\begin{aligned} & \frac{13 !}{3 ! 2 ! 3 !}=\frac{13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2}{3 \times 2 \times 2 \times 3 \times 2} \\ & \frac{13 !}{3 ! 2 ! 3 !}=13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 2 \times 5 \\ & \frac{13 !}{3 ! 2 ! 3 !}=86486400 \end{aligned}

Therefore, the total number of ways the letters are arranged is 86486400 ways.

 

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