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A word can have 9 identical letters and the remaining letters can all be different. If all the words that can be made with its letters are, then the word has 11880 different letters in total. 

Option: 1


Option: 2

4


Option: 3

12

 


Option: 4

16


Answers (1)

best_answer

Let the number of distinct letters other than identical letters be n.

The total letters will be n+9.

The number of ways in which they are arranged is given by,

\frac{(n+9)!}{9!}

Thus,

\frac{(n+9)!}{9!}=11880

\begin{aligned} &\begin{aligned} & (n+9)(n+8)(n+7) \ldots \ldots 11.10 .9=11880 \\ & (n+9)(n+8)(n+7) \ldots \ldots 11.10 .9=12 \times 11 \times 10 \times 9 \end{aligned}\\ &\begin{aligned} & n+9=12 \\ & n=3 \end{aligned} \end{aligned}

Therefore, the required number of different letters will be 3+1=4 ways.

Posted by

Ritika Kankaria

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